Question

A particle executes simple harmonic motion with a frequency v. The frequency with which the kinetic energy oscillates is
(a) v/2
(b) v
(c) 2 v
(d) zero

Answer 1

The frequency with which the kinetic energy oscillates is 2v (option c is correct)

1. The distance is given in the simple harmonic motion (SHM) is
2. $x= Asin(wt)$
3. The velocity is given as V=dx/dt
4. $V=Awcos(wt)$
5. The kinetic energy is given as
6. $K.E=\frac{1}{2}MV^{2}$
7. $K.E =\frac{1}{2}M A^{2}w^{2}cos^{2} (wt)$
8. $K.E =\frac{1}{2}M A^{2}w^{2}\frac{(1+cos(2wt))}{2} =\frac{1}{4}M A^{2}w^{2}(1+cos(2wt))$
9. The frequency of ossification is $2w$ .

Answer 2

The oscillation of the kinetic energy with which the frequency is 2v.

Explanation:

• The value of the kinetic energy changes to maximum from zero, twice. This is because of one complete oscillation.  
• In physics, a single oscillation is nothing but one complete cycle. So, over the term cycles, the term oscillation is preferred when there is rapid occurrence of cycles.
• Frequency is defined as the rate in which the cycles occurring via some units of time.