17.3 Kinematics of SHM

Displacement-Time Equation

The equation $a=-{\omega }^{2}x$ can be written as a second order differential equation by substituting acceleration, $a$ by the second derivative of displacement, $x$:

$$\begin{array}{rl}a& =-{\omega }^{2}x\\ \frac{d^{2}x}{d{t}^2}& =-{\omega }^{2}x\end{array}$$

A solution of this differential equation is:

$$x=x_o\sin \omega t$$

Where:

• $x$: displacement
• $x_o$: