{"id":250994,"date":"2022-09-10T10:35:08","date_gmt":"2022-09-10T05:05:08","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/question\/a-particle-in-s-h-m-is-described-by-the-displacement-function-xt-a-cos-%cf%89t-%ce%b8-if-the-initial-t-0-position-of-the-particle-is-i-cm-and-its-initial-velocity-is-%cf%80\/"},"modified":"2022-09-10T10:35:08","modified_gmt":"2022-09-10T05:05:08","slug":"a-particle-in-s-h-m-is-described-by-the-displacement-function-xt-a-cos-%cf%89t-%ce%b8-if-the-initial-t-0-position-of-the-particle-is-i-cm-and-its-initial-velocity-is-%cf%80","status":"publish","type":"questions","link":"https:\/\/infinitylearn.com\/surge\/question\/physics\/a-particle-in-shm-is-described-by-the-displacement-functi\/","title":{"rendered":"A particle in S.H.M. is described by the displacement function x(t) = a cos (\u03c9t\u00a0+\u00a0\u03b8).If the initial (t = 0) position of the particle is I cm and its initial velocity is\u00a0\u03c0\u00a0cm\/s. The angular frequency of the particle is\u00a0\u03c0\u00a0rad\/s, then its amplitude is"},"content":{"rendered":"","protected":false},"author":1,"template":"","meta":{"_yoast_wpseo_focuskw":"","_yoast_wpseo_title":"","_yoast_wpseo_metadesc":"A particle in S.H.M. is described by the displacement function x(t) = a cos (\u03c9t\u00a0+\u00a0\u03b8).If the initial (t = 0) position of the particle is I cm and its initial velocity is\u00a0\u03c0\u00a0cm\/s. The angular frequency of the particle is\u00a0\u03c0\u00a0rad\/s, then its amplitude is","custom_permalink":"question\/physics\/a-particle-in-shm-is-described-by-the-displacement-functi\/"},"categories":[],"acf":{"question":"

A particle in S.H.M. is described by the displacement function x(t) = a cos (\u03c9t<\/mi> <\/mo>+<\/mo> <\/mo>\u03b8<\/mi><\/math>).If the initial (t = 0) position of the particle is I cm and its initial velocity is \u03c0<\/mi> <\/mo>cm<\/mi>\/<\/mo>s<\/mi><\/math>. The angular frequency of the particle is \u03c0<\/mi> <\/mo>rad<\/mi>\/<\/mo>s<\/mi><\/math>, then its amplitude is<\/p>","options":[{"option":"

1 cm<\/p>","correct":false},{"option":"

2<\/mn> <\/mo><\/msqrt> <\/mo>cm<\/mi><\/math><\/p>","correct":true},{"option":"

2 cm<\/p>","correct":false},{"option":"

2.5 cm<\/p>","correct":false}],"solution":"

x<\/mi> <\/mo>=<\/mo> <\/mo>a<\/mi> <\/mo>cos<\/mi> <\/mo>(<\/mo>\u03c9t<\/mi> <\/mo>+<\/mo> <\/mo>\u03b8<\/mi>)<\/mo><\/math>------------(i)<\/p>

And v<\/mi> <\/mo>=<\/mo> <\/mo>dx<\/mi>dt<\/mi><\/mfrac> <\/mo>=<\/mo> <\/mo>-<\/mo>a\u03c9<\/mi> <\/mo>sin<\/mi>(<\/mo>\u03c9t<\/mi>+<\/mo>\u03b8<\/mi>)<\/mo><\/math>--------(ii)<\/p>

Given at t = 0, x = 1 cm and v = \u03c0<\/mi><\/math> and \u03c9<\/mi> <\/mo>=<\/mo> <\/mo>\u03c0<\/mi><\/math><\/p>

Putting these values in equation (i) and (ii), we will get<\/p>

sin<\/mi> <\/mo>\u03b8<\/mi> <\/mo>=<\/mo> <\/mo>-<\/mo>1<\/mn><\/mrow>a<\/mi><\/mfrac> <\/mo>and<\/mi> <\/mo>cos<\/mi> <\/mo>\u03b8<\/mi> <\/mo>=<\/mo> <\/mo>1<\/mn>A<\/mi><\/mfrac><\/math><\/p>

\u21d2<\/mo> <\/mo>sin<\/mi>2<\/mn><\/msup>\u03b8<\/mi> <\/mo>+<\/mo> <\/mo>cos<\/mi>2<\/mn><\/msup>\u03b8<\/mi> <\/mo>=<\/mo> <\/mo>(<\/mo>-<\/mo>1<\/mn>a<\/mi><\/mfrac>)<\/mo><\/mrow>2<\/mn><\/msup>+<\/mo>(<\/mo>1<\/mn>a<\/mi><\/mfrac>)<\/mo><\/mrow>2<\/mn><\/msup> <\/mo> <\/mo>\u21d2<\/mo> <\/mo>a<\/mi> <\/mo>=<\/mo> <\/mo>2<\/mn><\/msqrt> <\/mo>cm<\/mi><\/math><\/p>","subject":""},"yoast_head":"\nA particle in S.H.M. is described by the displacement function x(t) = a cos (\u03c9t\u00a0+\u00a0\u03b8).If the initial (t = 0) position of the particle is I cm and its initial velocity is\u00a0\u03c0\u00a0cm\/s. The angular frequency of the particle is\u00a0\u03c0\u00a0rad\/s, then its amplitude is - Infinity Learn by Sri Chaitanya<\/title>\n<meta name=\"description\" content=\"A particle in S.H.M. is described by the displacement function x(t) = a cos (\u03c9t\u00a0+\u00a0\u03b8).If the initial (t = 0) position of the particle is I cm and its initial velocity is\u00a0\u03c0\u00a0cm\/s. 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