Question

34. A particle is executing simple harmonic motion. Its displacement is given by

x = 5 sin pi t
where x is in cm and t in seconds. How long will the particle take to move from
the positon of equilibrium to the position of maximum displacement?
(1) 0.5s
2) 1.0s
3) 1.5s
4)2.0s​

Answer 1

Compare this to the standard equation for S.H.M:

x = A sin w t where w is the angular frequency.

So w = pi and since w = 2 pi f where f is the frequency

f = 1/2 and since T = 1/f then T = 2 sec for 1 complete cycle

Since it takes 1/4 cycle to move from minimum to maximum displacement

the required time is T/4 or t = 2 sec