A simple harmonic oscillator has a period T and energy E. the amplitude of the oscillator is doubled choose the correct answer
Correct answer: D. Period remain same, and Energy becomes 4 times.
- A. Period and energy get double.
- B. Period gets doubled while energy remain same
- C. Energy gets doubled while Period remain same
- D. Period remain same, and Energy becomes 4 times.
Explanation
The period (T) of a simple harmonic oscillator is independent of its amplitude. The period is solely determined by the mass of the object and the force constant (spring constant for a spring) according to the formula:T=2π√m/kWhere T is the period,m is the massand k is the force constant.Doubling the amplitude of a simple harmonic oscillator does not affect its mass or force constant, and therefore, the period remains the same.The energy (E) of a simple harmonic oscillator is proportional to the square of its amplitude according to the equation:E=1/2 kA2Where E is the energyk is the force constantA is the amplitude.If the amplitude is doubled, the energy becomes four times its original value.
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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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