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? A)10 m/s B)17 m/s C)25 m/s D)36 m/s E)More information is needed.

Question

Quizplus · Accepted Answer

We know that for a particle in simple harmonic motion, the maximum velocity is achieved when the acceleration is zero, which occurs at the equilibrium position. Therefore, we can use the equation for the maximum velocity in simple harmonic motion:

v_max = Aω

where A is the amplitude and ω is the angular frequency.

We are not given the amplitude, but we can relate it to the maximum acceleration using the equation:

a_max = Aω^2

Substituting the given values, we have:

400 = A(24)^2

Solving for A, we get:

A = 0.694 m

Finally, we can calculate the maximum velocity:

v_max = Aω = 0.694 x 24 = 16.656 ≈ 17 m/s.

Therefore, the answer is B.

A Particle in Simple Harmonic Motion Has an Angular Frequency