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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?

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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.

This problem has been solved

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