An object is undergoing simple harmonic motion. Its time period is T and total energy is E. The amplitude of vibration is reduced to half. What is the new time period and total energy of the system?
Correct answer: B. Time period = no change total energy = E/4
- A. Time period = T/2 total energy = E/4
- B. Time period = no change total energy = E/4
- C. Time period= T/2 total energy = E/2
- D. Time period= T total energy= E/2
Explanation
The time period does not depend on the amplitude but only on frequency. However, total energy varies proportionally to the square of the amplitude. So if amplitude reduces by half, energy reduces to (1/2)2 = 1/4
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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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