A particle executes SHM along a straight line. Its amplitude is A. The potential energy of the particle is equal to the kinetic energy when the displacement of the particle from the mean position is:
Correct answer: C. ±A/√2
- A. Zero
- B. ±A/2
- C. ±A/√2
- D. 2A
Explanation
When the potential energy is equal to the kinetic energy, we have:(1/2)kx^2 = (1/2)mv^2x^2 = (mv^2)/kv^2 = kx^2/mSubstituting v^2 into the expression for K, we have:K = (1/2)mv^2 = (1/2)m(kx^2/m) = (1/2)kx^2Thus, when the potential energy is equal to the kinetic energy, we have:2K = 2U2(1/2)kx^2 = (1/2)kA^2x^2 = A^2/2x = ±A/√2Therefore, the displacement of the particle from the mean position when the potential energy is equal to the kinetic energy is ±A/√2.lAs it is numerical, it can have only one possible answer.
This question appeared on the ETEA MDCAT 2017 paper, which you can sit online with every answer explained.
Report an error
The more specific you are, the faster it gets fixed. A source beats an opinion.
Prefer email? [email protected]
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.
Practise Waves
1,281 free Waves MCQs from Physics, each with the correct answer and an explanation. Unlimited attempts, no account needed.
Discussion
Stuck on an option, or know a faster way to get there? Ask or explain it here.
No comments yet. Be the first to explain this one.
Exams that ask Physics questions like this
Physics is on 16 papers prepared for on TestUstad, and all of them draw the same bank, so this question is worth knowing for every one of them.
More Simple Harmonic Motion questions
The time period of a simple pendulum is 2 seconds. If its length is increased by 4 times, then its period becomes:
A weight suspended from an ideal spring oscillates up and down with a period T. If the amplitude of the oscillation is doubled, the period will be:
The total energy of a particle executing S.H.M. is:
In S.H.M, the fraction of kinetic energy to total energy when displacement is one-half of the Amplitude is
The frequency of a second's pendulum is :
In Simple Harmonic Motion the acceleration of the particle is zero when its: