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#.