Question

An instantaneous displacement of a simple harmonic oscillator is \( x = A \cos(\omega t + \pi/4) \). Its speed will be maximum at time

• A. \( \frac{\pi}{4 \omega} \)
• B. \( \frac{\pi}{2 \omega} \)
• C. \( \frac{\pi}{\omega} \)
• D. \( \frac{2 \pi}{\omega} \)

Hint:

In simple harmonic motion, the speed is maximum when the sine function reaches its peak value of 1.

Answer 1

The Correct Option is A

Step 1: Speed in simple harmonic motion.
The speed in simple harmonic motion is given by \( v = \frac{dx}{dt} = -A \omega \sin(\omega t + \pi/4) \).
Step 2: Find the time when speed is maximum.
The speed is maximum when the sine function is equal to 1, i.e., at \( t = \frac{\pi}{4 \omega} \). Final Answer: \[ \boxed{\frac{\pi}{4 \omega}} \]