Question

Sol. [Key Concept: Classify each: $\sin^{2}\omega\ t$ is SHM ($T = \pi/\omega$); $\sin^{3}2\omega\ t$ periodic but not SHM; $sin\omega\ t + cos\pi\omega\ t$ non-periodic; $cos\omega\ t + cos2\omega\ t$ periodic, not SHM.]

(A) $\sin^{2}\omega t = \frac{1}{2} - \frac{1}{2}cos2\omega t$ it represents SHM motion having period $= \frac{\pi}{\omega}$

(B) $\sin^{3}2\omega t = \frac{3}{4}sin2\omega t - \frac{1}{4}sin6\omega t$

common period $\frac{\pi}{\omega}$ but not SHM.

(C) $sin\omega t + cos\pi\omega t \rightarrow$ no common period hence it is a nonperiodic function

(D) $cos\omega t + cos2\omega t$

common period $\frac{2\pi}{\omega}$ but it do not represent SHM.

$$A \rightarrow III,B \rightarrow I,C \rightarrow IV,D \rightarrow II $$