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A simple harmonic oscillator has an amplitude A and time period T. The time required by it to travel from x=A to x=A/2 is

Asked in CBSE AIPMT 1992 · Time, distance and displacement

Answer: (1) T/6

Step-by-step solution

Given: amplitude A, period T, starting at the extreme x=A.

Idea: measuring from the extreme, x=A cos ω t, so the phase does the timing.

A/2=A cos ω t, so cos ω t=1/2.

The smallest solution is ω t=π/3.

t=π/(3ω)=π/3×T/(2π)

t=T/6

Why the other options are wrong

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