A particle in simple harmonic motion has an angular frequency of 24 rad/s. Its maximum acceleration is 400 m/s2m/s2 . What is its maximum velocity
Question
A particle in simple harmonic motion has an angular frequency of 24 rad/s. Its maximum acceleration is 400 m/s². What is its maximum velocity?
Solution
The maximum velocity (Vmax) in simple harmonic motion can be calculated using the formula:
Vmax = ω * A
where ω is the angular frequency and A is the amplitude of the motion.
The amplitude can be found using the formula for maximum acceleration in simple harmonic motion:
Amax = ω² * A
Rearranging this formula, we get:
A = Amax / ω²
Substituting the given values:
A = 400 m/s² / (24 rad/s)² = 0.694 m
Now, we can find the maximum velocity:
Vmax = ω * A = 24 rad/s * 0.694 m = 16.656 m/s
So, the maximum velocity of the particle is 16.656 m/s.
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