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Question:

A particle undergoing simple harmonic motion has time dependent displacement given by x(t) = Asin(πt/90). The ratio of kinetic to potential energy of this particle at t = 210s will be :

13

3

19

1

Solution:

The correct option is C

Kinetic Energy, K = (1/2)mω²A²cos²(ωt)
Potential Energy, U = (1/2)mω²A²sin²(ωt)
K/U = cot²(ωt) = cot²(π/90)(210) = cot²(2π + π/3) = 1/3
Hence ratio is 1/3.
The correct option is C.