Question

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.

Answer 1

a_max = 50 cm/s^2

Step-by-step 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:

`x=Acos(\omega t)`

ω: angular velocity = 10 rad/s

A: amplitude = 5 cm

The acceleration is given by:

`a=\omega^2 x`

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

`a_(max)=\omega^2 x_(max)=\omega^2A`

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

`a_(max)=(10rad/s)^2(5cm)=50(cm)/(s^2)`

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