A particle executes simple harmonic oscillation with an amplitude A𝐴. The period of oscillation is T𝑇. The minimum time taken by the particle to travel half of the amplitude from the equilibrium position is
Question
A particle executes simple harmonic oscillation with an amplitude A𝐴. The period of oscillation is T𝑇. The minimum time taken by the particle to travel half of the amplitude from the equilibrium position is
Solution
The time period of a simple harmonic motion is divided into four equal parts as the particle goes from one extreme to the other extreme via the mean position.
So, the time taken to travel from the mean position to one extreme (which is the amplitude A) is T/4.
But in this case, we are asked to find the time taken to travel half of the amplitude. So, the particle travels half the distance in half the time.
Therefore, the minimum time taken by the particle to travel half of the amplitude from the equilibrium position is T/8.
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