Question

A particle executes SHM with amplitude 40 cm and time period 6 s. Minimum time to move from mean position to a point at 20 cm from extreme position is:

• A. 0.5 s
• B. 1.5 s
• C. 3 s
• D. 2.5 s

Hint:

Use phase method for SHM time problems.

Answer 1

The Correct Option is B

Step 1: Amplitude: \[ A = 40\ \text{cm} \]
Step 2: Point is 20 cm from extreme position: \[ x = A - 20 = 40 - 20 = 20\ \text{cm} \]
Step 3: SHM equation: \[ x = A\sin\theta \]
Step 4: \[ 20 = 40\sin\theta \Rightarrow \sin\theta = \frac{1}{2} \Rightarrow \theta = 30^\circ \]
Step 5: Angular frequency: \[ \omega = \frac{2\pi}{T} = \frac{2\pi}{6} \]
Step 6: Time: \[ t = \frac{\theta}{\omega} = \frac{\pi/6}{2\pi/6} = \frac{1}{2}\ \text{s} \]
Step 7: Minimum time corresponds to first reach: \[ t = 0.5\ \text{s} \]