Oscillation

Equilibrium Position

An equilibrium position is a point where an oscillating object experiences 0 resultant forces.

Complete Oscillation

A complete oscillation occurs when the vibrating object moves to and fro from its original position and moves in the same direction as its original motion.

Amplitude

Amplitude is the maximum displacement of an object from its equilibrium position. The SI unit for amplitude is meter, m.

Period

Period is defined as the time required for one complete oscillation or vibration.

Frequency

Frequency, f is the number of complete oscillations that take place in one second.

The SI unit for frequency is hertz, Hz.

Important Formula:

Displacement - Time Graph

From a Displacement - Time graph, we can find:

1. the amplitude
2. the period
3. the frequency

of an oscillation

Natural Frequency

The Natural frequency of an oscillating system is the frequency of the system when there is no external force acting on it.

Damping

• Damping is the decrease in the amplitude of an oscillating system.
• An oscillating system experiences damping when its energy is losing to the surrounding as heat energy.
• The frequency of the system remains unchanged.

Graph of Damping

The Displacement - Time Graph

The Amplitude - Time Graph

Internal and External Damping

Damping can be divided into:

• external damping, where an oscillating system loses energy to overcome frictional force or air resistance that act on it.
• internal damping, where an oscillating system loses energy due to the extension and compression of the molecules in the system.

Force Oscillation

In a damped oscillation, external force must be applied to the system to enable the oscillation to go on continuously.

Oscillation with the help of external force or forces is called a force oscillation.

Resonance

In a force oscillation, if the frequency of the external force is equal to the natural frequency of the system, the system will oscillates with maximum amplitude, and this is named as resonance.

Barton's Pendulum

When pendulum X oscillates, the other pendulums are forced to oscillate. Pendulum D will oscillates with the largest amplitude.

Pendulum X and D have equal length and consequently equal natural frequency. Therefore resonance happens to pendulum D, and it oscillates with maximum amplitude.