Simple harmonic motion

Displacement

The distance from the equilibrium position

Amplitude

The maximum displacement from the equilibrium position

Period

The time taken to complete one full oscillation

Frequency

The number of complete oscillations per unit time

Simple harmonic motion

• The acceleration of the object is directly proportional to its displacement And acts in the direction opposite to the displacement

Damping

An oscillation is damped when an external force that acts on the oscillator has the effect of reducing the amplitude of its oscillations. Energy is transferred to other forms.

Light damping

The amplitude of the oscillator gradually decrease with time, the period of the oscillations is almost unchanged.

Heavy damping

The amplitude decreases significantly, the period of the oscillation also increased slightly.

Very heavy damping

No oscillatory motion. Instead the oscillator would slowly move towards its equilibrium position.

Free oscillation

When a mechanical system is displaced from its equilibrium position and then allowed to oscillated without any external forces.

Forced oscillation

A periodic driver forces is applied to an oscillator. The object will vibrate at the driving frequency

Resonation

The driving frequency is equal to the natural frequency. The amplitude of the oscillations will increase dramatically.

Exponential decay

The amplitude of a damped oscillating system decreases exponentially with respect to time.

For resonation, as the amount of of damping increases:

The amplitude of the vibration decreases, the maximum amplitude occurs at a lower frequency, the peak on the graph becomes flatter and broader.

Isochronous

If an oscillation has a constant time period.