A particle executes S.H.M. with frequency f. The frequency of variation of its maximum or minimum kinetic energy is:
Correct answer: C. 2f
- A. f/2
- B. f
- C. 2f
- D. 4f
Explanation
K.E=½ mw2(x02-x2) = ½ mw2 (x02- x02sin2 wt) =½ mw2 x02(1-sin2 wt) =½ mw2 x02cos2 wt =½ mw2 x02(1+cos2 wt/2 ) =¼ mw2 x02 +¼ mw2 x02cos2wt =2f Hence the frequency of K.E. is 2ω or 2f In SHM, a particle has zero or minimum velocity at extreme points and maximum velocity at mean points. With the help of a diagram, we can see that in one time period of the pendulum (starting from the left extreme point) K.E. reaches zero to a maximum of two times. During one complete oscillation, the kinetic energy will become maximum twice. Therefore the frequency of kinetic energy will be 2f.
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About Simple Harmonic Motion
Simple harmonic motion is oscillation in which acceleration is directly proportional to displacement and directed toward the equilibrium position. Work includes displacement, velocity, acceleration, phase, period, frequency, amplitude and energy, with applications to springs and simple pendulums. The restoring force and the conditions for SHM distinguish it from general periodic motion.
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