If two S.H.M. are represented by equations y1=10sin3πt+π4 and y2=5sin3πt+3cos3πt then find the ratio of their amplitudes and phase difference in between them.

As y2=5sin3πt+3cos3πt=1012sin3πt+32cos3πt10cosπ3sin3πt+sinπ3cos3πt=10sin3πt+π3⇒A1A2=1010A1:A2=1:1 and Phase difference =π3-π4=π12rad

If two S.H.M. are represented by equations y1=10sin3πt+π4 and y2=5sin3πt+3cos3πt then find the ratio of their amplitudes and phase difference in between them.

As y2=5sin3πt+3cos3πt=1012sin3πt+32cos3πt10cosπ3sin3πt+sinπ3cos3πt=10sin3πt+π3⇒A1A2=1010A1:A2=1:1 and Phase difference =π3-π4=π12rad

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If two $S . H . M .$ are represented by equations $y_{1} = 10 \sin [3 π t + \frac{π}{4}]$ and $y_{2} = 5 [\sin (3 π t) + \sqrt{3} \cos (3 π t)]$ then find the ratio of their amplitudes and phase difference in between them.

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$A_{1} : A_{2} = 2 : 1$ ; $\frac{π}{10} r a d$

$A_{1} : A_{2} = 1 : 2$ ; $\frac{π}{12} r a d$

$A_{1} : A_{2} = 1 : 1$ ; $\frac{π}{12} r a d$

$A_{1} : A_{2} = 2 : 3$ ; $\frac{π}{14} r a d$

answer is C.

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As $y_{2} = 5 [\sin (3 π t) + \sqrt{3} \cos (3 π t)] = 10 [\frac{1}{2} \sin (3 π t) + \frac{\sqrt{3}}{2} \cos (3 π t)]$

$10 [\cos \frac{π}{3} \sin 3 π t + \sin \frac{π}{3} \cos 3 π t] = 10 \sin (3 π t + \frac{π}{3}) \Rightarrow \frac{A_{1}}{A_{2}} = \frac{10}{10}$

$A_{1} : A_{2} = 1 : 1$ and Phase difference $= \frac{π}{3} - \frac{π}{4} = \frac{π}{12} r a d$

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If two S.H.M. are represented by equations y1=10sin3πt+π4 and y2=5sin3πt+3cos3πt then find the ratio of their amplitudes and phase difference in between them.

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If two $S . H . M .$ are represented by equations $y_{1} = 10 \sin [3 π t + \frac{π}{4}]$ and $y_{2} = 5 [\sin (3 π t) + \sqrt{3} \cos (3 π t)]$ then find the ratio of their amplitudes and phase difference in between them.