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

Question

2n

n

#n/2#

3n

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Answer 1 · 2018-03-29T08:09:22

#2n#

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#.