Answer to Question #294311 in Physics for ilz man

Question

The equation of a particle executes s.h.m y=8sin (pi t+pi÷3)find a the amplitude

The period

Maximum velocity

Answer 1

Given:

$y=8\sin (\pi t+\pi/3)\:\rm cm$

The general equation of SHM is given by

$$y=A\sin\left (\frac{2\pi}{T} t+\phi_0\right)$$

(a) the amplitude

$$A=8\:\rm cm$$

(b) the period of oscillation

$$T=2\:\rm s$$

(c) maximum velocity

$$v_{\max}=A\omega=A*2\pi /T\\ =8*2\pi/2=8\pi \:\rm cm/s=25\: cm /s$$