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When the potential energy of a particle executing simple harmonic motion is one-fourth of the maximum value during the oscillation, its displacement from the equilibrium position in terms of amplitude ' $a$ ' is(a) $a / 4$ (b) $a / 3$ (c) $a / 2$ (d) $2 a / 3$
When the displacement of a particle executing simple harmonic motion is half its amplitude, the ratio of its kinetic energy to potential energy is ______.
When the displacement of a particle executing simple harmonic motion is half its amplitude, the ratio of its kinetic energy to potential energy is 3 : 1.
Explanation:
x = A cos ωt
x = `"A"/2`
we get ωt = 60°
`"KE"/"PE" = (1/2 "m"ω^2"A"^2 sin^2 ω"t")/(1/2 "m"ω^2"A"^2 cos ω"t")`
= tan2 ωt
= tan2 60°
= 3
Concept: Energy in Simple Harmonic Motion
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