Question

A simple pendulum performs simple harmonic motion about x = 0 with an amplitude a and time period T. The time taken by the pendulum to reach x = a/2 from the mean postion will be:
1. T/6
2. 6/T
3. 12/T
4. T/12

Answer 1

Correct Answer - Option 4 : T/12

CONCEPT:

Simple harmonic motion

• Simple Harmonic Motion or SHM is defined as a motion in which the restoring force is directly proportional to the displacement of the body from its mean position.
  • The direction of this restoring force is always towards the mean position.
• Amplitude: It is the maximum displacement of the particle.
• Time period: The minimum time after which the particle keeps on repeating its motion is known as the time period.
• The equation of simple harmonic motion is given as,

⇒ y = a sinωt

Where y = displacement at time t, a = amplitude, and ω = angular frequency

CALCULATION:

Given y = a/2​

• The displacement of the simple pendulum performs simple harmonic motion is given as,

⇒ y = a sinωt

⇒ a/2 = a sinωt

\(\Rightarrow sin(\frac{\pi}{6})=sin (\frac{2\pi}{T}\times t)\)

\(\Rightarrow \frac{\pi}{6}=\frac{2\pi}{T}\times t \\\Rightarrow t =\frac{T}{12}\)

• Hence, option 4 is correct.