Question

Two particles \(A\) and \(B\) are executing simple harmonic motion with amplitudes \(10\,\text{cm}\) and \(20\,\text{cm}\) respectively. If the time periods of two particles \(A\) and \(B\) are \(8\,\text{s}\) and \(12\,\text{s}\) respectively, then the ratio of the times taken by the particles \(A\) and \(B\) to complete \(\dfrac18^{\text{th}}\) oscillation starting from their extreme positions is

• A. \(1:2\)
• B. \(1:1\)
• C. \(3:4\)
• D. \(2:3\)

Hint:

The time taken to complete any fraction of an oscillation is \[ \boxed{t=\left(\text{Fraction of oscillation}\right)\times T.} \] It depends only on the time period \(T\) and is independent of the amplitude.

Answer 1

The Correct Option is D