Oscillations Ques 68
68. Out of the following functions, representing motion of a particle, which represents $SHM$ ?
[2011]
(A) $y=\sin \omega t-\cos \omega t$
(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)
Show Answer
Answer:
Correct Answer: 68.(c)
Solution:
- (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 $\theta=\tan ^{-1} \frac{B}{A}$
BETA
