Simple harmonic motion (SHM)

Definition

Simple Harmonic Motion (SHM) is a type of periodic motion where the restoring force is directly proportional to the displacement and acts in the direction opposite to that of displacement. It is characterized by its sinusoidal oscillations in time.

5 Must Know Facts For Your Next Test

1. The equation of motion for SHM is $x(t) = A \cos(\omega t + \phi)$, where $A$ is amplitude, $\omega$ is angular frequency, and $\phi$ is phase constant.
2. The period ($T$) of SHM is given by $T = \frac{2\pi}{\omega}$.
3. In SHM, the total mechanical energy (sum of potential and kinetic energy) remains constant.
4. The maximum speed in SHM occurs as it passes through the equilibrium position, and the maximum acceleration occurs at the extremes of motion.
5. Examples of SHM include a mass-spring system and a simple pendulum for small angles.

Review Questions

• What is the relationship between restoring force and displacement in Simple Harmonic Motion?
• Write down the equation of motion for SHM and define each term.
• How does the total mechanical energy behave in a system undergoing Simple Harmonic Motion?

Related terms

Amplitude:

The maximum displacement from the equilibrium position in oscillatory motion.

Angular Frequency:

$\omega = \frac{2\pi}{T}$; it measures how many radians per second an object undergoes during its oscillation cycle.

Phase Constant:

$\phi$; a term that represents an initial angle at $t=0$, determining where in its cycle the oscillation begins.