Physics - SHM Question with Solution | TestHub

With zero phase constant,$y=A\sin \frac{2\pi t}{T},v=v_{\max }\cos \frac{2\pi t}{T}$

(A) At y = A/2,$\cos \theta =\frac{\sqrt{3}}{2}\Rightarrow v=\frac{\sqrt{3}}{2}{v}_{\max }>\frac{v_{\max }}{2}$correct.

(B)$v=\frac{v_{\max }}{2}\Rightarrow \cos \theta =\frac{1}{2}\Rightarrow y=A\sin \theta =\frac{\sqrt{3}}{2}A>\frac{A}{2}$correct.

(C) At t = T/8,$y=A\sin \frac{\pi }{4}=\frac{A}{\sqrt{2}}>\frac{A}{2}$correct.

(D) y = A/2 first at$\theta =\pi /6\Rightarrow t=\frac{T}{12}<\frac{T}{8}$correct.

All four are correct.