The energy of a simple harmonic oscillator at a displacement 'a' is partly kinetic and partly potential. The energy of simple harmonic oscillator remains constant everywhere, which one of the following option will be correct about the simple harmonic oscillator.
Correct answer: B. P.E is maximum at extreme position
- A. K.E is maximum at extreme position
- B. P.E is maximum at extreme position
- C. Both K.E and P.E are minimum at mean position
- D. P.E is maximum at mean position
Explanation
In simple harmonic motion, the formula for kinetic energy and potential energy are as below: K.E=1/2mv2(a2-x2) and U=1/2mv2x2Step1: Formula of kinetic and potential energy for simple harmonic motionIn simple harmonic motion, the formula for kinetic energy and potential energy are as below:K.E=1/2mv2(a2-x2) and U= 1/2mω2x2 Step2: Find values at the mean positionwhere m is mass, a is the amplitude of the particle, and x is the distance from the mean position.At the mean position, x will be zero. =>K= 1/2mω2a2 and U=0.So, the value of kinetic energy will be maximum and potential energy is zero. That is the minimum 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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