The amplitude of a particle executing simple harmonic motion is 5cm, while its angular velocity is 10 rads -1 . Calculate the magnitude of the maximum acceleration of the particle.

a_max = 50 cm/s^2

Explanation:

To find the magnitude of the maximum acceleration of the particle, you take into account the equation of motion in a simple harmonic motion:

ω: angular velocity = 10 rad/s

A: amplitude = 5 cm

The acceleration is given by:

and the maximum acceleration is obtained when the cosine function is maximum, that is, when cos(wt) = 1. Then, you have:

Then, you replace the values of w and A in order to calculate a_max:

hence, the maximum acceleration is 50 cm/s^2