Concepts Of Physics MCQ Edition [Volume 1]PhysicsSimple Harmonic Motion

A particle travels along the X-axis governed by the equation x = x₀ ^2 t . The motion is simple harmonic

Options

Awith amplitude x₀
Bwith time period
Cwith amplitude 2x₀
Dwith time period 2

Correct answer

B. with time period

Step-by-step solution

Given equation of motion is x = x₀ ^2 t . Using the trigonometric identity ^2 = 1 - 2 2 , the equation can be rewritten as: x = x₀ 2 (1 - 2 t) x - x₀ 2 = - x₀ 2 2 t This represents simple harmonic motion about the mean position x = x₀ 2 . The amplitude of the SHM is A = x₀ 2 . The angular frequency of the SHM is ' = 2 . The time period of the motion is T = 2 ' = 2 2 = .

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