Question

A mass is performing simple harmonic motion. You may assume that there are no significant frictional forces in this problem (the motion is undamped). The maximum speed of the mass during the motion is 4.6 m/s . The amplitude of the motion is 25 cm

Part A.)  

What is ? , the angular frequency of this motion?

Express your answer using two significant figures.

Part B.)  

What is T? , the period of this motion?    

Express your answer using two significant figures.

Part C.)  

What is the maximum acceleration of the mass during this motion?

Express your answer using two significant figures.

Answer 1

It is given that:

1) The mass is performing simple harmonic motion(SHM).

2) Maximum speed of the mass, V_m =4.6m/s.

3) The amplitude of the motion, a=25cm =0.25m

SOLUTION:

1)The formula for maximum velocity in SHM is :

V_m = w×a.............. where w- angular velocity.

therefore angular velocity,

w=v/a=4.6/0.25= 18.4radian/second.

2)Now,

The angular velocity is given by,

w=2?/T .........where T- time period of SHM.

Therefore,T=2?/w=2?/18.5= 0.34seconds.

3)The maximum acceleration is given by,

Acceleration=a×w² = 0.25×4.6² =5.29m/s.