Which of the following expression does not represent SHM?

Question

Which of the following expression does not represent SHM? (A) A cos ω t (B) A sin 2 ω t (C) A sin ω t+B cos ω t (D) A sin 2 ω t

Tardigrade Admin · Accepted Answer

For SHM , (d2 y/d t2) propto-y If y=A sin 2 ω t (d y/d t) =(2 A sin ω t cos ω t) ω =A ω sin 2 ω t (d2 y/d t2) =+2 A ω2 cos 2 ω t i.e., (d2 y/d t2) is not proportional to -y.

Q. Which of the following expression does not represent SHM?

$A cos ω t$

$A sin 2 ω t$

$A sin ω t + B cos ω t$

$A sin^{2} ω t$

For $S H M, \frac{d ^{2} y}{d t ^{2}} \propto - y$
If $y = A sin^{2} ω t$
$\frac{d y}{d t} = (2 A sin ω t cos ω t) ω$
$= A ω sin 2 ω t$
$\frac{d ^{2} y}{d t ^{2}} = + 2 A ω^{2} cos 2 ω t$
i.e., $\frac{d ^{2} y}{d t ^{2}}$ is not proportional to $- y$ .

Q. Which of the following expression does not represent SHM?

Acosωt

Asin2ωt

Asinωt+Bcosωt