A frequency of variation of kinetic energy of a simple harmonic motion of frequency n is?

  1. 2n
  2. n
  3. n/2
  4. 3n

1 Answer
Mar 29, 2018

2n

Explanation:

The velocity of a simple harmonic oscillator varies as

v_0 sin(2pi n t +phi)

The kinetic energy is

K = 1/2 m v^2 = 1/2mv_0^2 sin^2(2pi n t +phi)

Now, sin^2 theta = 1/2(1-cos(2theta)) and so, we have

K = 1/2mv_0^2 ( 1/2-1/2 cos(4pi n t +2phi))
qquad =1/4mv_0^2-1/4 mv_0^2 cos(2pi (2n) t +2phi)

Here, the time dependence comes from the last term and its frequency is 2n.