What should be the ratio of kinetic energy to total energy for a simple harmonic oscillator?
Correct answer: A. 1 β (x 2 / xo 2 )
- A. 1 β (x 2 / xo 2 )
- B. 1
- C. (xo 2 β x 2 )
- D. Β½ (x 2)
Explanation
πΎπΈ = 1 2 πΟ 2 (π₯ 0 2 β π₯ 2 ) πππ‘ππ πΈπππππ¦ = 1 2 πΟ 2 π₯ 0 2 Dividing the two terms gives us the ratio and the solution to the equationKE/E = 1 - (x^2/xo^2)Where x is the displacement from the equilibrium position and xo is the amplitude of the oscillation.This means that the ratio of kinetic energy to total energy is given by 1 minus the square of displacement divided by the square of the amplitude.Therefore, the correct answer is:1 - (x^2/xo^2)
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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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