Answer to Question #225634 in Physics for Ella

Question

Define simple harmonic motion and give the expressions for the velocity and acceleration of such motion at the different points along it's path

Answer 1

Simple harmonic motion is a kind of motion that occurs periodically. Such motion can be described with sine or cosine function.

Velocity at any point:

$$v(t)=v_\text{max}\cos(\omega t),$$

Acceleration:

$$a(t)=-a_\text{max}\sin(\omega t)=\\-\omega v_\text{max}\sin(\omega t).$$