Oscillations - Result Question 8

11. Out of the following functions, representing motion of a particle, which represents SHM?

(A) $y=\sin \omega t-\cos \omega t$

[2011]

(B) $y=\sin ^{3} \omega t$

(C) $y=5 \cos (\frac{3 \pi}{4}-3 \omega t)$

(D) $y=1+\omega t+\omega^{2} t^{2}$

(a) Only (A)

(b) Only (D) does not represent SHM

(c) Only (A) and (C)

(d) Only (A) and (B)

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Answer:

Correct Answer: 11. (c)

Solution:

  1. (c) Only functions given in (A) & (C) represent SHM. $y=A \sin \omega t+B \cos \omega t \Rightarrow y=a \sin (\omega t+\phi)$. This is also a equation of S.H.M where $\phi=\sqrt{A^{2}+B^{2}}$

$A=a \cos \phi, B=a \sin \phi$ and $\theta=\tan ^{-1} \frac{B}{A}$