Question

Displacement of a particle executing simple harmonic motion is represented by $Y=0.08\sin ⟮3\pi t+\frac{\pi }{4}⟯$ metre. Then calculate:-
(a) Time period.
(b) Initial phase
(c) Displacement from mean position at t = $\frac{7}{36}$ sec.

Answer 1

Displacement equation is given as $Y=0.08\sin (3\pi t+\frac{\pi }{4})$

On comparing with $Y=A\sin (wt+\pi )$

We get, $w=3\pi$ and $\varphi =\frac{\pi }{4}$

Time period $T=\frac{2\pi }{T}=\frac{2\pi }{3\pi }=\frac{2}{3}s$

Initial phase $\varphi =\frac{\pi }{4}$

At $t=\frac{7}{36}s$, $Y=0.08\sin (3\pi \times \frac{7}{36}+\frac{\pi }{4})=0.08\sin \left(5\pi /6\right)$

$⟹Y=0.08\times 0.5=0.04m$