Answer to Question #250520 in Physics for Alonge Emmanuel

Question

If a body moving with simple harmonic motion has an angular velocity of 50 radians per second and an amplitude of 10cm, calculate its linear velocity.

Answer 1

The displacement of the body in SHM is given in general as follows:

$$x(t) = A\sin(\omega t)$$

where $A = 10cm$ is the amplitude, and $\omega = 50rad/s$ is the angular velocity and $t$ is time. The linear velocity, by definition, is the derivative from the displacement:

$$v(t) = \dfrac{d}{dt}(x(t)) = \dfrac{d}{dt}(A\sin(\omega t)) = A\omega \cos(\omega t)$$

Answer. The linear velocity at any given time is: $v(t) = A\omega \cos(\omega t)$, where $A = 10cm$ is the amplitude, and $\omega = 50rad/s$ is the angular velocity and $t$ is time.