Question

The amplitude and frequency of an object executing simple harmonic motion are 0.01 m and 12 Hz respectively. What is the velocity of object at displacement 0.005 m? What is the maximum velocity of the object?

Answer 1

The velocity of object at displacement 0.005 m is

$v=\omega \sqrt{(A^2-x^2)}=2\pi f \sqrt{(A^2-x^2)}$

$=2\pi (12) \sqrt{((0.01)^2-(0.005)^2)}=0.653 m/s$

The maximum velocity is

$v_{max}=\omega A=2\pi f A$

$=2\pi (12)(0.01)=0.75 m/s$