Physics - SHM Question with Solution | TestHub

Ans. (A, C, D)

Initial phase difference $=\frac{\pi }{3}$ and since time period is same thus phase difference remains constant. Also, ${\mathrm{X}}_{\mathrm{P}}=\mathrm{A}\sin \left(\omega \mathrm{t}+\frac{5\pi }{6}\right)\Rightarrow {\mathrm{v}}_{\mathrm{P}}=\mathrm{A}\omega \cos \left(\omega \mathrm{t}+\frac{5\pi }{6}\right)$ ${\mathrm{X}}_{\mathrm{Q}}=2\mathrm{A}\sin \left(\omega \mathrm{t}+\frac{\pi }{2}\right)\Rightarrow {\mathrm{v}}_{\mathrm{Q}}=2\mathrm{A}\omega \cos \left(\omega \mathrm{t}+\frac{\pi }{2}\right)$

$\therefore {\mathrm{X}}_{\mathrm{P}}={\mathrm{X}}_{\mathrm{Q}}$ at $\mathrm{t}=\frac{\mathrm{T}}{2}$ for first time.

Also sep. between then is maximum when ${\mathrm{V}}_{\mathrm{P}}={\mathrm{V}}_{\mathrm{Q}}$