Question:
An instantaneous displacement of a simple harmonic oscillator is \( x = A \cos(\omega t + \pi/4) \). Its speed will be maximum at time
An instantaneous displacement of a simple harmonic oscillator is \( x = A \cos(\omega t + \pi/4) \). Its speed will be maximum at time
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In simple harmonic motion, the speed is maximum when the sine function reaches its peak value of 1.
Updated On: Mar 24, 2026
- \( \frac{\pi}{4 \omega} \)
- \( \frac{\pi}{2 \omega} \)
- \( \frac{\pi}{\omega} \)
- \( \frac{2 \pi}{\omega} \)
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The Correct Option is A
Solution and Explanation
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: \[ \boxed{\frac{\pi}{4 \omega}} \]
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