In S.H.M, the fraction of kinetic energy to total energy when displacement is one-half of the Amplitude is
Correct answer: D. 3/4
- A. 1/8
- B. 1/2
- C. 1/4
- D. 3/4
Explanation
Correct option is D)In case of SHMKE= 1/2 mω^2 (a ^2 −x ^2 ) and at x=a/2KE= 1/2 mω ^2 [a^2 −(a/2)^2 ]= 3/4 [ 1/2 mω^2 ^ 2 ]Total energy = 1/2 mω^2 a^2 ∴ Fraction of total energy= KE/Total energy = 3/4 [1 /2 mω^2 a^2 ] = 3/4 1/2mωa^2As it is numerical, it can have only one answer.
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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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