{"id":2566,"date":"2022-03-24T16:30:42","date_gmt":"2022-03-24T16:30:42","guid":{"rendered":"https:\/\/stage-wp.10minuteschool.com\/?p=2566"},"modified":"2022-04-16T12:00:07","modified_gmt":"2022-04-16T06:00:07","slug":"%e0%a6%b8%e0%a6%b0%e0%a6%b2-%e0%a6%a6%e0%a7%8b%e0%a6%b2%e0%a6%a8-%e0%a6%97%e0%a6%a4%e0%a6%bf-%e0%a6%b8%e0%a6%82%e0%a6%95%e0%a7%8d%e0%a6%b0%e0%a6%be%e0%a6%a8%e0%a7%8d%e0%a6%a4-%e0%a6%ac%e0%a6%bf","status":"publish","type":"post","link":"https:\/\/10minuteschool.com\/content\/%e0%a6%b8%e0%a6%b0%e0%a6%b2-%e0%a6%a6%e0%a7%8b%e0%a6%b2%e0%a6%a8-%e0%a6%97%e0%a6%a4%e0%a6%bf-%e0%a6%b8%e0%a6%82%e0%a6%95%e0%a7%8d%e0%a6%b0%e0%a6%be%e0%a6%a8%e0%a7%8d%e0%a6%a4-%e0%a6%ac%e0%a6%bf\/","title":{"rendered":"\u09b8\u09b0\u09b2 \u09a6\u09cb\u09b2\u09a8 \u0997\u09a4\u09bf \u09b8\u0982\u0995\u09cd\u09b0\u09be\u09a8\u09cd\u09a4 \u09ac\u09bf\u09ad\u09bf\u09a8\u09cd\u09a8 \u09b0\u09be\u09b6\u09bf \u0964 Some terms related to simple oscillation motion"},"content":{"rendered":"

\u09b8\u09b0\u09b2 \u09a6\u09cb\u09b2\u09a8 \u0997\u09a4\u09bf\u09b0 \u0985\u09a8\u09cd\u09a4\u09b0\u0995 \u09b8\u09ae\u09c0\u0995\u09b0\u09a3\u09c7\u09b0 \u098f\u0995\u099f\u09bf \u09b8\u09ae\u09be\u09a7\u09be\u09a8 \u09a4\u09a5\u09be \u09b8\u09b0\u09b2 \u09a6\u09cb\u09b2\u09a8 \u0997\u09a4\u09bf \u09b8\u09ae\u09cd\u09aa\u09a8\u09cd\u09a8 \u0995\u09a3\u09be\u09b0 \u0997\u09a4\u09bf\u09b0 \u09b8\u09ae\u09c0\u0995\u09b0\u09a3 \u09b9\u099a\u09cd\u099b\u09c7,\u00a0<\/span><\/p>\n

x=A \\sin (\\omega t+\\delta)<\/span><\/span><\/p>\n

\u09aa\u09b0\u09cd\u09af\u09be\u09df\u0995\u09be\u09b2, T (Time period)\u00a0<\/b><\/h2>\n

\u09b8\u09b0\u09b2 \u09a6\u09cb\u09b2\u09a8 \u0997\u09a4\u09bf \u09b8\u09ae\u09cd\u09aa\u09a8\u09cd\u09a8 \u0995\u09cb\u09a8\u09cb \u0995\u09a3\u09be\u09b0 \u098f\u0995\u099f\u09bf \u09aa\u09c2\u09b0\u09cd\u09a3 \u09a6\u09cb\u09b2\u09a8 \u09b8\u09ae\u09cd\u09aa\u09a8\u09cd\u09a8 \u09b9\u09a4\u09c7 \u09af\u09c7 \u09b8\u09ae\u09df \u09b2\u09be\u0997\u09c7 \u09a4\u09be\u0995\u09c7 \u09a4\u09be\u09b0 \u09aa\u09b0\u09cd\u09af\u09be\u09df\u0995\u09be\u09b2 T \u09ac\u09b2\u09c7<\/span>\u0964<\/span><\/p>\n

\u09b8\u09b0\u09b2 \u09a6\u09cb\u09b2\u09a8 \u0997\u09a4\u09bf \u09b8\u09ae\u09cd\u09aa\u09a8\u09cd\u09a8 \u0995\u09a3\u09be\u09b0 \u0997\u09a4\u09bf\u09b0 \u09b8\u09ae\u09c0\u0995\u09b0\u09a3\u09c7 \u09b8\u09ae\u09df t<\/span><\/span> \u0995\u09c7 \\frac{2\\pi}{\\omega}<\/span><\/span> \u09aa\u09b0\u09bf\u09ae\u09be\u09a3 \u09ac\u09c3\u09a6\u09cd\u09a7\u09bf \u0995\u09b0\u09be \u09b9\u09b2\u09c7 \u09b8\u09b0\u09a3 \u09b9\u09df<\/span><\/p>\nx^{\\prime}=A \\sin \\left[\\omega\\left(t+\\frac{2 \\pi}{\\omega}\\right)+\\delta\\right] \\\\\n\n\\quad=A \\sin (\\omega t+2 \\pi+\\delta)=A \\sin (\\omega t+\\delta) \\\\\n\n\\therefore x^{\\prime}=x<\/span>\n

\u09a6\u09c7\u0996\u09be \u09af\u09be\u099a\u09cd\u099b\u09c7 \u09af\u09c7, \\frac{2 \\pi}{\\omega}<\/span><\/span> \u09b8\u09ae\u09df \u09aa\u09b0 \u09b8\u09b0\u09a3\u09c7\u09b0 \u09ae\u09be\u09a8 \u098f\u0995\u0987 \u09b9\u099a\u09cd\u099b\u09c7 \u0985\u09b0\u09cd\u09a5\u09be\u09ce \\frac{2 \\pi}{\\omega}<\/span><\/span> \u09b8\u09ae\u09df \u09aa\u09b0 \u09aa\u09b0 \u09b0\u09be\u09b6\u09bf\u099f\u09bf\u09b0 \u09aa\u09c1\u09a8\u09b0\u09be\u09ac\u09c3\u09a4\u09cd\u09a4\u09bf \u0998\u099f\u099b\u09c7<\/span>\u0964<\/span> \u09b8\u09c1\u09a4\u09b0\u09be\u0982 \\frac{2 \\pi}{\\omega}<\/span><\/span> \u09b9\u099a\u09cd\u099b\u09c7 \u09b8\u09b0\u09b2 \u09a6\u09cb\u09b2\u09a8 \u0997\u09a4\u09bf\u09b0 \u09aa\u09b0\u09cd\u09af\u09be\u09df\u0995\u09be\u09b2 T<\/span><\/span>\u0964<\/span><\/p>\n

\\therefore T=\\frac{2 \\pi}{\\omega}<\/span><\/span><\/p>\n

\u09aa\u09b0\u09cd\u09af\u09be\u09df\u0995\u09be\u09b2 \u0993 \u09ac\u09b2 \u09a7\u09cd\u09b0\u09c1\u09ac\u0995\u09c7\u09b0 \u09b8\u09ae\u09cd\u09aa\u09b0\u09cd\u0995 (The relation of\u00a0 time period and force constant)<\/b><\/h2>\n

\u0986\u09ae\u09b0\u09be \u099c\u09be\u09a8\u09bf, \\omega^{2}=\\frac{k}{m}<\/span><\/span>\u0964<\/span> \u09b8\u09c1\u09a4\u09b0\u09be\u0982 T=\\frac{2 \\pi}{\\omega}<\/span><\/span>\u00a0\u09b8\u09ae\u09c0\u0995\u09b0\u09a3\u09c7 \u09a6\u09be\u0981\u09dc\u09be\u09df,<\/span><\/p>\n

\\therefore T=2 \\pi \\sqrt{\\frac{\\mathrm{m}}{k}}<\/span><\/span><\/p>\n

\u098f \u09b8\u09ae\u09c0\u0995\u09b0\u09a3 \u09a5\u09c7\u0995\u09c7 \u09a6\u09c7\u0996\u09be \u09af\u09be\u09df \u09af\u09c7, \u09b8\u09b0\u09b2 \u09a6\u09cb\u09b2\u09a8 \u0997\u09a4\u09bf\u09b0 \u09aa\u09b0\u09cd\u09af\u09be\u09df\u0995\u09be\u09b2 \u09b8\u09cd\u09aa\u09a8\u09cd\u09a6\u09a8\u09b6\u09c0\u09b2 \u0995\u09a3\u09be\u099f\u09bf\u09b0 \u09ad\u09b0 m<\/span><\/span> \u098f\u09ac\u0982 \u09ac\u09b2 \u09a7\u09cd\u09b0\u09c1\u09ac\u0995 k<\/span> \u098f\u09b0 \u09b8\u09be\u09a5\u09c7 \u09b8\u09ae\u09cd\u09aa\u09b0\u09cd\u0995\u09bf\u09a4<\/span>\u0964<\/span> \u09af\u09c7\u09b9\u09c7\u09a4\u09c1 \u0995\u09cb\u09a8\u09cb \u0995\u09a3\u09be\u09b0 \u09ad\u09b0 m<\/span><\/span> \u09a8\u09bf\u09b0\u09cd\u09a6\u09bf\u09b7\u09cd\u099f,<\/span><\/p>\n

\\therefore T \\propto \\frac{1}{\\sqrt{k}}<\/span><\/span><\/p>\n

\u0985\u09b0\u09cd\u09a5\u09be\u09ce \u09b8\u09b0\u09b2 \u09a6\u09cb\u09b2\u09a8 \u0997\u09a4\u09bf \u09b8\u09ae\u09cd\u09aa\u09a8\u09cd\u09a8 \u0995\u09cb\u09a8\u09cb \u0995\u09a3\u09be\u09b0 \u09aa\u09b0\u09cd\u09af\u09be\u09df\u0995\u09be\u09b2 \u09ac\u09b2 \u09a7\u09cd\u09b0\u09c1\u09ac\u0995\u09c7\u09b0 \u09ac\u09b0\u09cd\u0997\u09ae\u09c2\u09b2\u09c7\u09b0 \u09ac\u09cd\u09af\u09be\u09b8\u09cd\u09a4\u09be\u09a8\u09c1\u09aa\u09be\u09a4\u09bf\u0995<\/span>\u0964<\/span><\/p>\n

\u0995\u09ae\u09cd\u09aa\u09be\u0999\u09cd\u0995, f<\/span><\/b>\u00a0<\/span>(Frequency)<\/b><\/h2>\n

\u0995\u09cb\u09a8\u09cb \u09b8\u09b0\u09b2 \u09a6\u09cb\u09b2\u09a8 \u0997\u09a4\u09bf \u09b8\u09ae\u09cd\u09aa\u09a8\u09cd\u09a8 \u0995\u09a3\u09be \u098f\u0995\u0995 \u09b8\u09ae\u09df\u09c7 \u09af\u09c7 \u0995\u09df\u099f\u09bf \u09aa\u09c2\u09b0\u09cd\u09a3 \u09a6\u09cb\u09b2\u09a8 \u09ac\u09be \u0995\u09ae\u09cd\u09aa\u09a8 \u09b8\u09ae\u09cd\u09aa\u09a8\u09cd\u09a8 \u0995\u09b0\u09c7 \u09a4\u09be\u0995\u09c7 \u09a4\u09be\u09b0 \u0995\u09ae\u09cd\u09aa\u09be\u0999\u09cd\u0995 f<\/span><\/span> \u09ac\u09b2\u09c7<\/span>\u0964<\/span><\/p>\n

\\therefore f=\\frac{1}{T}=\\frac{\\omega}{2 \\pi}=\\frac{1}{2 \\pi} \\sqrt{\\frac{k}{m}}<\/span><\/span><\/p>\n

\u0995\u09cc\u09a3\u09bf\u0995 \u0995\u09ae\u09cd\u09aa\u09be\u0999\u09cd\u0995, <\/b>(Angular Frequency)<\/b><\/h2>\n

\u09b8\u09b0\u09b2 \u09a6\u09cb\u09b2\u09a8 \u0997\u09a4\u09bf\u09b8\u09ae\u09cd\u09aa\u09a8\u09cd\u09a8 \u0995\u09cb\u09a8\u09cb \u0995\u09a3\u09be \u098f\u0995\u0995 \u09b8\u09ae\u09df\u09c7 \u09af\u09c7 \u0995\u09cc\u09a3\u09bf\u0995 \u09a6\u09c2\u09b0\u09a4\u09cd\u09ac \u0985\u09a4\u09bf\u0995\u09cd\u09b0\u09ae \u0995\u09b0\u09c7 \u09a4\u09be\u0995\u09c7 \u0995\u09cc\u09a3\u09bf\u0995 \u0995\u09ae\u09cd\u09aa\u09be\u0999\u09cd\u0995 <\/span> \u09ac\u09b2\u09c7<\/span>\u0964<\/span><\/p>\n

\u09aa\u09b0\u09cd\u09af\u09be\u09df\u0995\u09be\u09b2 \u098f\u09ac\u0982 \u0995\u09ae\u09cd\u09aa\u09be\u0999\u09cd\u0995 \u09af\u09a5\u09be\u0995\u09cd\u09b0\u09ae\u09c7 T<\/span><\/span> \u098f\u09ac\u0982 f<\/span><\/span> \u09b9\u09b2\u09c7,<\/span><\/p>\n\\omega=\\frac{2 \\pi}{T}=2 \\pi f=\\sqrt{\\frac{k}{m}}<\/span>\n

\u0995\u09cc\u09a3\u09bf\u0995 \u0995\u09ae\u09cd\u09aa\u09be\u0999\u09cd\u0995 \\omega<\/span> <\/span>\u098f\u09b0 \u09ae\u09be\u09a4\u09cd\u09b0\u09be \u09b9\u099a\u09cd\u099b\u09c7 T^{-1}<\/span><\/span> \u098f\u09ac\u0982 \u098f\u0995\u0995 \u09b0\u09c7\u09a1\u09bf\u09df\u09be\u09a8\/\u09b8\u09c7\u0995\u09c7\u09a8\u09cd\u09a1 \\left(\\mathrm{rad} \\mathrm{s}^{-1}\\right)<\/span><\/span><\/p>\n

\u09ac\u09bf\u09b8\u09cd\u09a4\u09be\u09b0, A<\/span> (Expansion)\u00a0<\/b><\/h2>\n

x=A \\sin (\\omega t+\\delta)<\/span><\/span> \u09b8\u09ae\u09c0\u0995\u09b0\u09a3\u09c7\u09b0 \u09a7\u09cd\u09b0\u09c1\u09ac\u0995 A<\/span> \u098f\u09b0 \u098f\u0995\u099f\u09bf \u09b8\u09b0\u09b2 \u09ad\u09cc\u09a4 \u09a4\u09be\u09ce\u09aa\u09b0\u09cd\u09af \u0986\u099b\u09c7\u0964 \u0986\u09ae\u09b0\u09be \u099c\u09be\u09a8\u09bf, <\/span>sine<\/span> \u0985\u09aa\u09c7\u0995\u09cd\u09b7\u0995\u09c7\u09b0 \u09ae\u09be\u09a8 -1 \u09a5\u09c7\u0995\u09c7 +1 \u09aa\u09b0\u09cd\u09af\u09a8\u09cd\u09a4 \u09b9\u09a4\u09c7 \u09aa\u09be\u09b0\u09c7\u0964 \u0995\u09be\u099c\u09c7\u0987 \u09ae\u09a7\u09cd\u09af\u09ac\u09b0\u09cd\u09a4\u09c0 \u09b8\u09be\u09ae\u09cd\u09af\u09be\u09ac\u09b8\u09cd\u09a5\u09be\u09a8 (x=0)<\/span><\/span> \u09a5\u09c7\u0995\u09c7 \u09b8\u09b0\u09a3 x<\/span><\/span> \u098f\u09b0 \u09b8\u09b0\u09cd\u09ac\u09cb\u099a\u09cd\u099a \u09ae\u09be\u09a8 \u09b9\u09a4\u09c7 \u09aa\u09be\u09b0\u09c7 A<\/span><\/span>\u0964<\/span> \u09af\u09c7\u09b9\u09c7\u09a4\u09c1 \u0995\u09cb\u09a8\u09cb \u0995\u09a3\u09be \u09b8\u09be\u09ae\u09cd\u09af\u09be\u09ac\u09b8\u09cd\u09a5\u09be\u09a8 \u09a5\u09c7\u0995\u09c7 \u09af\u09c7\u0995\u09cb\u09a8\u09cb \u098f\u0995 \u09a6\u09bf\u0995\u09c7 \u09af\u09c7 \u09b8\u09b0\u09cd\u09ac\u09cb\u099a\u09cd\u099a \u09a6\u09c2\u09b0\u09a4\u09cd\u09ac \u0985\u09a4\u09bf\u0995\u09cd\u09b0\u09ae \u0995\u09b0\u09c7 \u09a4\u09be\u0995\u09c7 \u09ac\u09bf\u09b8\u09cd\u09a4\u09be\u09b0 A<\/span> \u09ac\u09b2\u09c7, \u09b8\u09c1\u09a4\u09b0\u09be\u0982 A<\/span> \u09b9\u099a\u09cd\u099b\u09c7 \u09b8\u09b0\u09b2 \u09a6\u09cb\u09b2\u09a8 \u0997\u09a4\u09bf\u09b0 \u09ac\u09bf\u09b8\u09cd\u09a4\u09be\u09b0\u0964<\/span><\/p>\n

\u09a6\u09b6\u09be,<\/b> (Phase) (\\omega t+\\delta)<\/span><\/b><\/h2>\n

\u09b8\u09b0\u09b2 \u09a6\u09cb\u09b2\u09a8 \u0997\u09a4\u09bf\u09b8\u09ae\u09cd\u09aa\u09a8\u09cd\u09a8 \u0995\u09cb\u09a8\u09cb \u0995\u09a3\u09be\u09b0 \u09a6\u09b6\u09be \u09ac\u09b2\u09a4\u09c7 \u0990 \u0995\u09a3\u09be\u09b0 \u09af\u09c7\u0995\u09cb\u09a8\u09cb \u09ae\u09c1\u09b9\u09c2\u09b0\u09cd\u09a4\u09c7 \u0997\u09a4\u09bf\u09b0 \u09b8\u09ae\u09cd\u09af\u0995 \u0985\u09ac\u09b8\u09cd\u09a5\u09be \u09ac\u09cb\u099d\u09be\u09af\u09bc\u0964 \u0995\u09cb\u09a8\u09cb \u098f\u0995\u099f\u09bf \u09ae\u09c1\u09b9\u09c2\u09b0\u09cd\u09a4\u09c7 \u0997\u09a4\u09bf\u09b0 \u09b8\u09ae\u09cd\u09af\u0995 \u0985\u09ac\u09b8\u09cd\u09a5\u09be \u09ac\u09b2\u09a4\u09c7 \u0990 \u09ac\u09bf\u09b6\u09c7\u09b7 \u09ae\u09c1\u09b9\u09c2\u09b0\u09cd\u09a4\u09c7 \u09ac\u09b8\u09cd\u09a4\u09c1 \u0995\u09a3\u09be\u099f\u09bf\u09b0 \u09b8\u09b0\u09a3, \u09ac\u09c7\u0997, \u09a4\u09cd\u09ac\u09b0\u09a3, \u09ac\u09b2 \u0987\u09a4\u09cd\u09af\u09be\u09a6\u09bf \u09ac\u09cb\u099d\u09be\u09af\u09bc\u0964 \u09b8\u09b0\u09b2 \u09a6\u09cb\u09b2\u09a8 \u0997\u09a4\u09bf \u09b8\u09ae\u09cd\u09aa\u09a8\u09cd\u09a8 \u0995\u09a3\u09be\u09b0 \u0997\u09a4\u09bf\u09b0 \u09b8\u09ae\u09c0\u0995\u09b0\u09a3\u09c7\u09b0 (\\omega t+\\delta)<\/span><\/span>\u00a0<\/span>\u09b0\u09be\u09b6\u09bf\u099f\u09bf \u09b9\u099a\u09cd\u099b\u09c7 \u0997\u09a4\u09bf\u09b0 \u09a6\u09b6\u09be (<\/span>Phase<\/span>)<\/span>\u0964<\/span> \u09a7\u09cd\u09b0\u09c1\u09ac\u0995 <\/span> \u09b9\u09b2\u09cb \u09a6\u09b6\u09be \u09a7\u09cd\u09b0\u09c1\u09ac\u0995\u0964 \u098f\u0995\u0987 \u09ac\u09bf\u09b8\u09cd\u09a4\u09be\u09b0 \u098f\u09ac\u0982 \u0995\u09ae\u09cd\u09aa\u09be\u0999\u09cd\u0995\u09c7\u09b0 \u0995\u09bf\u09a8\u09cd\u09a4\u09c1 \u09ad\u09bf\u09a8\u09cd\u09a8 \u09a6\u09b6\u09be\u09b0 \u098f\u0995\u09be\u09a7\u09bf\u0995 \u0997\u09a4\u09bf \u09b9\u09a4\u09c7 \u09aa\u09be\u09b0\u09c7\u0964<\/span><\/p>\n

\u09af\u09c7\u09ae\u09a8, \\delta=0^{\\circ}<\/span><\/span>\u00a0\u09b9\u09b2\u09c7<\/span><\/p>\nx=A \\sin (\\omega t+\\delta)=A \\sin \\left(\\omega t+0^{\\circ}\\right)<\/span>\n

\u09ac\u09be<\/span>, x=A \\sin \\omega t<\/span><\/span><\/p>\n

\u098f\u0996\u09a8<\/span>, t=0<\/span><\/span> \u09b9\u09b2\u09c7 \u09b8\u09b0\u09a3 x=0<\/span><\/span>\u0964<\/span> \u0985\u09b0\u09cd\u09a5\u09be\u09ce \u098f\u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0\u09c7 \u0995\u09a3\u09be\u099f\u09bf\u09b0 \u0997\u09a4\u09bf \u09b6\u09c1\u09b0\u09c1 \u09b9\u09df \u09a4\u09be\u09b0 \u09b8\u09be\u09ae\u09cd\u09af\u09be\u09ac\u09b8\u09cd\u09a5\u09be\u09a8 \u09a5\u09c7\u0995\u09c7<\/span>\u0964<\/span><\/p>\n

\u0986\u09ac\u09be\u09b0, \\delta=\\pi \/ 2<\/span><\/span>\u00a0\u09b9\u09b2\u09c7<\/span><\/p>\nx=A \\sin (\\omega t+\\delta)=A \\sin (\\omega t+\\pi \/ 2)<\/span>\n

\u09b8\u09c1\u09a4\u09b0\u09be\u0982 t=0<\/span><\/span>\u00a0<\/span>\u09b8\u09ae\u09af\u09bc\u09c7 x=A<\/span><\/span>\u00a0<\/span>\u0985\u09b0\u09cd\u09a5\u09be\u09ce \u09b8\u09b0\u09a3 x<\/span><\/span> \u09b9\u099a\u09cd\u099b\u09c7 \u09b8\u09b0\u09cd\u09ac\u09cb\u099a\u09cd\u099a\u0964 \u098f\u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0\u09c7 \u0995\u09a3\u09be\u099f\u09bf\u09b0 \u0997\u09a4\u09bf \u09b6\u09c1\u09b0\u09c1 \u09b9\u09af\u09bc \u098f\u0995 \u09aa\u09cd\u09b0\u09be\u09a8\u09cd\u09a4 \u09a5\u09c7\u0995\u09c7\u0964 \u0985\u09a8\u09cd\u09af \u09a6\u09b6\u09be \u09a7\u09cd\u09b0\u09c1\u09ac\u0995\u09c7\u09b0 \u099c\u09a8\u09cd\u09af \u0985\u09a8\u09cd\u09af \u0986\u09a6\u09bf \u09b8\u09b0\u09a3 \u09aa\u09be\u0993\u09af\u09bc\u09be \u09af\u09be\u09af\u09bc\u0964<\/span><\/p>\n

\u0995\u09a3\u09be\u099f\u09bf\u09b0 \u0986\u09a6\u09bf \u0985\u09ac\u09b8\u09cd\u09a5\u09be\u09a8 \u098f\u09ac\u0982 \u09a6\u09cd\u09b0\u09c1\u09a4\u09bf \u09a6\u09cd\u09ac\u09be\u09b0\u09be \u09b8\u09b0\u09b2 \u09a6\u09cb\u09b2\u09a8 \u0997\u09a4\u09bf\u09b0 \u09ac\u09bf\u09b8\u09cd\u09a4\u09be\u09b0 A<\/span> \u098f\u09ac\u0982 \u09a6\u09b6\u09be \u09a7\u09cd\u09b0\u09c1\u09ac\u0995 <\/span> \u09a8\u09bf\u09b0\u09cd\u09a3\u09c0\u09a4 \u09b9\u09af\u09bc\u0964 \u098f \u09a6\u09c1\u0987 \u0986\u09a6\u09bf \u09b6\u09b0\u09cd\u09a4 \u09a6\u09cd\u09ac\u09be\u09b0\u09be \u09b8\u09a0\u09bf\u0995\u09ad\u09be\u09ac\u09c7 A<\/span> \u098f\u09ac\u0982 <\/span> \u098f\u09b0 \u09ae\u09be\u09a8 \u09a8\u09bf\u09b0\u09cd\u09a7\u09be\u09b0\u09bf\u09a4 \u09b9\u09af\u09bc\u0964 \u098f\u0995\u09ac\u09be\u09b0 \u0997\u09a4\u09bf \u09b6\u09c1\u09b0\u09c1 \u09b9\u09b2\u09c7 \u0985\u09ac\u09b6\u09cd\u09af \u098f\u0995\u099f\u09bf \u09a8\u09bf\u09b0\u09cd\u09a6\u09bf\u09b7\u09cd\u099f \u0995\u09ae\u09cd\u09aa\u09be\u0999\u09cd\u0995\u09c7\u09b0 \u09b8\u09cd\u09aa\u09a8\u09cd\u09a6\u09a8\u09b6\u09c0\u09b2 \u0995\u09a3\u09be\u09b0 \u09ac\u09bf\u09b8\u09cd\u09a4\u09be\u09b0 \u0993 \u09a6\u09b6\u09be \u09a7\u09cd\u09b0\u09c1\u09ac\u0995 \u09a7\u09cd\u09b0\u09c1\u09ac \u09a5\u09be\u0995\u09c7, \u09af\u09a6\u09bf \u09a8\u09be \u0985\u09a8\u09cd\u09af\u09be\u09a8\u09cd\u09af \u09ac\u09b2 \u0995\u09cd\u09b0\u09bf\u09af\u09bc\u09be \u0995\u09b0\u09c7\u0964<\/span><\/p>\n

\u09ac\u09c7\u0997, v<\/span> (Velocity)<\/b><\/h2>\n

x=A \\sin (\\omega t+\\delta)<\/span><\/span> \u09b8\u09ae\u09c0\u0995\u09b0\u09a3\u0995\u09c7 \u09b8\u09ae\u09df\u09c7\u09b0 \u09b8\u09be\u09aa\u09c7\u0995\u09cd\u09b7\u09c7 \u0985\u09a8\u09cd\u09a4\u09b0\u09c0\u0995\u09b0\u09a3 \u0995\u09b0\u09c7 \u09b8\u09b0\u09b2 \u09a6\u09cb\u09b2\u09a8 \u0997\u09a4\u09bf \u09b8\u09ae\u09cd\u09aa\u09a8\u09cd\u09a8 \u0995\u09a3\u09be\u09b0 \u09ac\u09c7\u0997 v<\/span> \u09aa\u09be\u0993\u09df\u09be \u09af\u09be\u09df<\/span>\u0964<\/span><\/p>\nv=\\frac{d x}{d t}=\\omega A \\cos (\\omega t+\\delta)<\/span>\n

\u09b8\u09b0\u09b2 \u09a6\u09cb\u09b2\u09a8 \u0997\u09a4\u09bf\u09b0 \u09b8\u09ae\u09c0\u0995\u09b0\u09a3 x=B \\cos (\\omega t+\\delta)<\/span><\/span>\u00a0\u09a7\u09b0\u09be \u09b9\u09b2\u09c7,<\/span><\/p>\n

\u09ac\u09c7\u0997 v<\/span> \u09b9\u09df, v=\\frac{d x}{d t}=-\\omega \\mathrm{B} \\sin (\\omega t+\\delta)<\/span><\/span><\/p>\n

\u09ac\u09c7\u0997 \u0993 \u09b8\u09b0\u09a3\u09c7\u09b0 \u09b8\u09ae\u09cd\u09aa\u09b0\u09cd\u0995 (The relation between velocity and displacement)<\/b><\/h3>\n

\u09ac\u09c7\u0997 v=\\frac{d x}{d t}=-\\omega \\mathrm{B} \\sin (\\omega t+\\delta)<\/span><\/span><\/p>\nv=\\omega A \\sqrt{1-\\sin ^{2}(\\omega t+\\delta)}<\/span>\n=\\omega A \\sqrt{1-\\frac{x^{2}}{A^{2}}}<\/span>\n=\\omega A \\sqrt{\\frac{A^{2}-x^{2}}{A^{2}}}<\/span>\n

\u09ac\u09be, v=\\omega \\sqrt{A^{2}-x^{2}}<\/span><\/p>\n

\u098f \u09b8\u09ae\u09c0\u0995\u09b0\u09a3 \u09a5\u09c7\u0995\u09c7 \u09a6\u09c7\u0996\u09be \u09af\u09be\u09af\u09bc \u09af\u09c7, \u09b8\u09b0\u09b2 \u09a6\u09cb\u09b2\u09a8 \u0997\u09a4\u09bf \u09b8\u09ae\u09cd\u09aa\u09a8\u09cd\u09a8 \u0995\u09a3\u09be\u09b0 \u09ac\u09c7\u0997 v<\/span> \u09a4\u09be\u09b0 \u09b8\u09b0\u09a3 x<\/span><\/span> \u098f\u09b0 \u0989\u09aa\u09b0 \u09a8\u09bf\u09b0\u09cd\u09ad\u09b0\u09b6\u09c0\u09b2\u0964 \u09af\u0996\u09a8 x=0<\/span><\/span>, \u0985\u09b0\u09cd\u09a5\u09be\u09ce \u0995\u09a3\u09be\u099f\u09bf \u09af\u0996\u09a8 \u09ae\u09a7\u09cd\u09af\u09ac\u09b0\u09cd\u09a4\u09c0 \u09b8\u09be\u09ae\u09cd\u09af\u09be\u09ac\u09b8\u09cd\u09a5\u09be\u09a8 \u0985\u09a4\u09bf\u0995\u09cd\u09b0\u09ae \u0995\u09b0\u09c7, <\/span>\u09a4\u0996\u09a8 v=\\omega \\sqrt{A^{2}-0}=\\omega A<\/span><\/span>\u00a0\u09b9\u09df \u098f\u09ac\u0982 \u098f\u099f\u09bf\u0987 \u09ac\u09c7\u0997\u09c7\u09b0 \u09b8\u09b0\u09cd\u09ac\u09a8\u09bf\u09ae\u09cd\u09a8 \u09ae\u09be\u09a8\u0964<\/span><\/p>\n\\therefore v_{\\max }=\\omega A<\/span>\n

\u09b8\u09c1\u09a4\u09b0\u09be\u0982 \u09ae\u09a7\u09cd\u09af\u09ac\u09b0\u09cd\u09a4\u09c0 \u09b8\u09be\u09ae\u09cd\u09af\u09be\u09ac\u09b8\u09cd\u09a5\u09be\u09a8\u09c7 \u09b8\u09b0\u09b2 \u09a6\u09cb\u09b2\u09a8 \u0997\u09a4\u09bf \u09b8\u09ae\u09cd\u09aa\u09a8\u09cd\u09a8 \u0995\u09a3\u09be\u09b0 \u09ac\u09c7\u0997 \u09b8\u09b0\u09cd\u09ac\u09cb\u099a\u09cd\u099a\u0964<\/span><\/p>\n

\u09af\u0996\u09a8 x=A<\/span><\/span>,<\/span> \u0985\u09b0\u09cd\u09a5\u09be\u09ce \u0995\u09a3\u09be\u099f\u09bf \u09af\u0996\u09a8 \u09ac\u09bf\u09b8\u09cd\u09a4\u09be\u09b0\u09c7\u09b0 \u09aa\u09cd\u09b0\u09be\u09a8\u09cd\u09a4\u09c7 \u0989\u09aa\u09b8\u09cd\u09a5\u09bf\u09a4 \u09b9\u09af\u09bc,\u00a0<\/span>\u09a4\u0996\u09a8 v=\\omega \\sqrt{A^{2}-A^{2}}=0<\/span><\/span> \u098f\u09ac\u0982 \u098f\u099f\u09bf\u0987 \u09ac\u09c7\u0997\u09c7\u09b0 \u09b8\u09b0\u09cd\u09ac\u09a8\u09bf\u09ae\u09cd\u09a8 \u09ae\u09be\u09a8\u0964<\/span><\/p>\n\\therefore v_{\\min }=0<\/span>\n

\u09b8\u09c1\u09a4\u09b0\u09be\u0982 \u09ac\u09bf\u09b8\u09cd\u09a4\u09be\u09b0\u09c7\u09b0 \u09aa\u09cd\u09b0\u09be\u09a8\u09cd\u09a4\u09c7 \u09ae\u09c1\u09b9\u09c1\u09b0\u09cd\u09a4\u09c7\u09b0 \u099c\u09a8\u09cd\u09af \u0995\u09a3\u09be\u099f\u09bf\u09b0 \u09ac\u09c7\u0997 \u09b6\u09c2\u09a8\u09cd\u09af \u09b9\u09af\u09bc \u098f\u09ac\u0982 \u0997\u09a4\u09bf\u09b0 \u09a6\u09bf\u0995 \u09aa\u09be\u09b2\u09cd\u099f\u09be\u09af\u09bc\u0964<\/span><\/p>\n

\u0985\u09a4\u098f\u09ac, \u09b8\u09b0\u09b2 \u09a6\u09cb\u09b2\u09a8 \u0997\u09a4\u09bf \u09b8\u09ae\u09cd\u09aa\u09a8\u09cd\u09a8 \u0995\u09cb\u09a8\u09cb \u0995\u09a3\u09be\u09b0 \u09ac\u09c7\u0997 \u09ae\u09a7\u09cd\u09af\u09ac\u09b0\u09cd\u09a4\u09c0 \u09b8\u09be\u09ae\u09cd\u09af\u09be\u09ac\u09b8\u09cd\u09a5\u09be\u09a8\u09c7 \u09b8\u09b0\u09cd\u09ac\u09cb\u099a\u09cd\u099a \u09b9\u09af\u09bc \u098f\u09ac\u0982 \u09b8\u09b0\u09a3 \u09ac\u09c3\u09a6\u09cd\u09a7\u09bf\u09b0 \u09b8\u09be\u09a5\u09c7 \u09b8\u09be\u09a5\u09c7 \u09ac\u09c7\u0997 \u09b9\u09cd\u09b0\u09be\u09b8 \u09aa\u09c7\u09a4\u09c7 \u09a5\u09be\u0995\u09c7 \u098f\u09ac\u0982 \u09ac\u09bf\u09b8\u09cd\u09a4\u09be\u09b0\u09c7\u09b0 \u09aa\u09cd\u09b0\u09be\u09a8\u09cd\u09a4\u09c7 \u09ac\u09c7\u0997 \u09b6\u09c2\u09a8\u09cd\u09af \u09b9\u09af\u09bc\u0964<\/span><\/p>\n

\u09a4\u09cd\u09ac\u09b0\u09a3, a<\/span><\/b>\u00a0<\/span>(Acceleration)<\/b><\/h2>\n

v=-\\omega \\mathrm{B} \\sin (\\omega t+\\delta)<\/span> \u09b8\u09ae\u09c0\u0995\u09b0\u09a3\u0995\u09c7 \u09b8\u09ae\u09df\u09c7\u09b0 \u09b8\u09be\u09aa\u09c7\u0995\u09cd\u09b7\u09c7 \u0985\u09a8\u09cd\u09a4\u09b0\u09c0\u0995\u09b0\u09a3 \u0995\u09b0\u09c7 \u0986\u09ae\u09b0\u09be \u09a4\u09cd\u09ac\u09b0\u09a3 a<\/span><\/span> \u09aa\u09be\u0987,<\/span><\/p>\na=\\frac{d v}{d t}=-\\omega^{2} \\mathrm{~A} \\sin (\\omega t+\\delta)<\/span>\n

\u09b8\u09b0\u09b2 \u09a6\u09cb\u09b2\u09a8 \u0997\u09a4\u09bf\u09b0 \u09b8\u09ae\u09c0\u0995\u09b0\u09a3 x=\\mathrm{B} \\cos (\\omega t+\\delta)<\/span><\/span> \u09a7\u09b0\u09be \u09b9\u09b2\u09c7,\u00a0<\/span>\u09a4\u09cd\u09ac\u09b0\u09a3, a=\\frac{d v}{d t}=-\\omega^{2} B \\cos (\\omega t+\\delta)<\/span><\/span><\/p>\n

\u09a4\u09cd\u09ac\u09b0\u09a3 \u0993 \u09b8\u09b0\u09a3\u09c7\u09b0 \u09b8\u09ae\u09cd\u09aa\u09b0\u09cd\u0995 (The relation between Acceleration and Displacement )<\/b><\/h3>\n

\u09a4\u09cd\u09ac\u09b0\u09a3, a=\\frac{d v}{d t}=-\\omega^{2} B \\cos (\\omega t+\\delta)<\/span><\/span> \u09a5\u09c7\u0995\u09c7 \u09b2\u09c7\u0996\u09be \u09af\u09be\u09df, a=-\\omega^{2} x<\/span><\/span><\/p>\n

\u098f \u09b8\u09ae\u09c0\u0995\u09b0\u09a3 \u09a5\u09c7\u0995\u09c7\u0993 \u09a6\u09c7\u0996\u09be \u09af\u09be\u09af\u09bc, \u09b8\u09b0\u09b2 \u09a6\u09cb\u09b2\u09a8 \u0997\u09a4\u09bf \u09b8\u09ae\u09cd\u09aa\u09a8\u09cd\u09a8 \u0995\u09cb\u09a8\u09cb \u0995\u09a3\u09be\u09b0 \u09a4\u09cd\u09ac\u09b0\u09a3 a<\/span><\/span> \u09a4\u09be\u09b0 \u09b8\u09b0\u09a3 x<\/span><\/span> \u098f\u09b0 \u0989\u09aa\u09b0 \u09a8\u09bf\u09b0\u09cd\u09ad\u09b0\u09b6\u09c0\u09b2\u0964<\/span><\/p>\n

\u09af\u0996\u09a8 x=0<\/span><\/span>, \u0985\u09b0\u09cd\u09a5\u09be\u09ce \u0995\u09a3\u09be\u099f\u09bf \u09af\u0996\u09a8 \u09ae\u09a7\u09cd\u09af\u09ac\u09b0\u09cd\u09a4\u09c0 \u09b8\u09be\u09ae\u09cd\u09af\u09be\u09ac\u09b8\u09cd\u09a5\u09be\u09a8 \u0985\u09a4\u09bf\u0995\u09cd\u09b0\u09ae \u0995\u09b0\u09c7, \u09a4\u0996\u09a8 a=0<\/span><\/span>, \u098f\u09ac\u0982 \u098f\u099f\u09bf\u0987 \u09a4\u09cd\u09ac\u09b0\u09a3\u09c7\u09b0 \u09b8\u09b0\u09cd\u09ac\u09a8\u09bf\u09ae\u09cd\u09a8 \u09ae\u09be\u09a8<\/span>\u0964<\/span><\/p>\n\\therefore a_{\\min }=0<\/span>\n

\u0986\u09ac\u09be\u09b0, \u09af\u0996\u09a8 x=A<\/span><\/span>, \u0985\u09b0\u09cd\u09a5\u09be\u09ce \u0995\u09a3\u09be\u099f\u09bf \u09af\u0996\u09a8 \u09ac\u09bf\u09b8\u09cd\u09a4\u09be\u09b0\u09c7\u09b0 \u09aa\u09cd\u09b0\u09be\u09a8\u09cd\u09a4\u09c7 \u0989\u09aa\u09b8\u09cd\u09a5\u09bf\u09a4 \u09b9\u09df, \u09a4\u0996\u09a8 a=-\\omega^{2} A<\/span> <\/span>\u098f\u09ac\u0982 \u098f\u099f\u09bf \u09a4\u09cd\u09ac\u09b0\u09a3\u09c7\u09b0 \u09b8\u09b0\u09cd\u09ac\u09cb\u099a\u09cd\u099a \u09ae\u09be\u09a8<\/span>\u0964<\/span> \u098b\u09a3\u09be\u09a4\u09cd\u09ae\u0995 \u099a\u09bf\u09b9\u09cd\u09a8 \u09ac\u09cb\u099d\u09be\u09df \u09a4\u09cd\u09ac\u09b0\u09a3 \u09b8\u09b0\u09a3\u09c7\u09b0 \u09ac\u09bf\u09aa\u09b0\u09c0\u09a4\u09ae\u09c1\u0996\u09c0<\/span>\u0964<\/span><\/p>\n\\therefore a_{\\max }=\\omega^{2} A<\/span>\n

\u0985\u09a4\u098f\u09ac, \u09b8\u09b0\u09b2 \u09a6\u09cb\u09b2\u09a8 \u0997\u09a4\u09bf \u09b8\u09ae\u09cd\u09aa\u09a8\u09cd\u09a8 \u0995\u09a3\u09be\u09b0 \u09a4\u09cd\u09ac\u09b0\u09a3 \u09ae\u09a7\u09cd\u09af\u09ac\u09b0\u09cd\u09a4\u09c0 \u09b8\u09be\u09ae\u09cd\u09af\u09be\u09ac\u09b8\u09cd\u09a5\u09be\u09a8\u09c7 \u09b6\u09c2\u09a8\u09cd\u09af \u09b9\u09df \u098f\u09ac\u0982 \u09b8\u09b0\u09a3 \u09ac\u09c3\u09a6\u09cd\u09a7\u09bf\u09b0 \u09b8\u09be\u09a5\u09c7 \u09b8\u09be\u09a5\u09c7 \u09a4\u09cd\u09ac\u09b0\u09a3 \u09ac\u09c3\u09a6\u09cd\u09a7\u09bf \u09aa\u09c7\u09a4\u09c7 \u09a5\u09be\u0995\u09c7 \u098f\u09ac\u0982 \u09ac\u09bf\u09b8\u09cd\u09a4\u09be\u09b0\u09c7\u09b0 \u09aa\u09cd\u09b0\u09be\u09a8\u09cd\u09a4\u09c7 \u09a4\u09cd\u09ac\u09b0\u09a3 \u09b8\u09b0\u09cd\u09ac\u09cb\u099a\u09cd\u099a \u09b9\u09df<\/span>\u0964<\/span><\/p>\n

\u09b8\u09b0\u09cd\u09ac\u09cb\u099a\u09cd\u099a \u09b8\u09b0\u09a3, \u09a6\u09cd\u09b0\u09c1\u09a4\u09bf \u098f\u09ac\u0982 \u09a4\u09cd\u09ac\u09b0\u09a3(Maximum Displacement, Speed and Acceleration)<\/b><\/h3>\n

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\u09b8\u09c1\u09a4\u09b0\u09be\u0982, \\left.\\begin{array}{l}\n\nx_{\\max }=A \\\\\n\nv_{\\max }=\\omega A \\\\\n\na_{\\max }=\\omega^{2} A\n\n\\end{array}\\right\\}<\/span><\/span><\/p>\n

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Read More<\/a><\/p>\n","protected":false},"author":56,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[51,4242,3028,50],"tags":[1870,1881,1019,1121,1267,1119,1859,1883,1871,1120,1882],"_links":{"self":[{"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/posts\/2566"}],"collection":[{"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/users\/56"}],"replies":[{"embeddable":true,"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/comments?post=2566"}],"version-history":[{"count":7,"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/posts\/2566\/revisions"}],"predecessor-version":[{"id":13262,"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/posts\/2566\/revisions\/13262"}],"wp:attachment":[{"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/media?parent=2566"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/categories?post=2566"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/tags?post=2566"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}