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PHY 104 PHY 104 Past Questions Objective Question
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Question

If the kinetic energy of a particle executing S.H.M. is given by K = K₀ cos²(αt), then the displacement of the particle is given by
Options
A x = √(K₀/(mω²)) sin(αt)
B x = √(2K₀/(mω²)) sin(αt)
Correct Answer
C x = √(2ω²/(mK₀)) sin(αt)
D x = √(2K₀/(mω)) sin(αt)
Correct Answer

Option B is the correct answer.

Detailed Explanation

The kinetic energy in SHM is K = ½mω²(A² - x²). Also, K = ½mω²A² cos²(ωt). Given K = K₀ cos²(αt), so ½mω²A² = K₀, and ω = α. Then A = √(2K₀/(mω²)). Displacement x = A sin(ωt) = √(2K₀/(mω²)) sin(αt).

Hint

Recall the expression for kinetic energy in SHM: K = ½mω²A² sin²(ωt) or cos²(ωt).

Question Info

Course: PHY 104
Topic: PHY 104 Past Questions
Type: Objective
Difficulty: Not specified
Question 804 of 947
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