Question

An object is undergoing shm with the maximum displacement of 16 cm and an angular frequency of 0.040 s^-1 assume that at t= 0 it is at its maximum displacement at which of these times will it have its maximum speed

a) 20 second

b) 39 seconds

C) 56 seconds

D) 78 seconds

e) 157 seconds

PLEASE SHOW WORK CLEARLY

Answer 1

Given that max displacement of object is 16 cm, So

A = Amplitude = 16 cm = 0.16 m

Angular frequency = w = 0.040 s^-1

At t = 0 object is at maximum displacement

Now time period of object moving in SHM will be:

T = 2*pi/w

T = 2*pi/0.040 = 157.08 sec

Now we need time when object will have maximum speed:

Since given that object starts at t = 0 from it's maximum displacement, And in SHM motion object have maximum velocity at equilibrium position, So as per definition of time period,

time taken by object to move from maximum displacement to equilibrium will be equal to 'T/4'

So,

t1 = T/4 = 157.08/4

T = 39.3 sec = approx 39 sec

After that at T/2 object will again have max displacement, then after another T/4 time at

t2 = T/2 + T/4 = 3T/4

at t = 3T/4 object will again be at equilibrium, So

t2 = 3*157.08/4 = 117.8 sec

So only one option is correct. that is Option B.

Let me know if you've any query.