Harmonic Motion 5.5

Define, in words, simple harmonic motion.

• Acceleration is proportional to displacement from the equilibrium position;

• and is always directed towards the equilibrium position.

For an oscillating body, state what is meant by forced frequency.

The frequency at which an object is made to oscillate.

For an oscillating body, state what is meant by natural frequency of vibration.

The frequency at which an object oscillates when free to do so.

Distinguish between free oscillations and forced oscillations.

• Free oscillations: the body oscillates without any loss of energy

• Forced oscillations: a continuous energy input by an external periodic force is required to make the body oscillate

For simple harmonic motion, describe the difference between displacement and amplitude.

• Displacement is the distance of the body from the equilibrium position;

• whereas amplitude is the maximum displacement.

For simple harmonic motion, describe the difference between frequency and angular frequency.

• Frequency is the number of oscillations per unit time;

• whereas angular frequency is the product of 2π x frequency.

Explain what is meant by a resonance of a mechanical system.

• Resonance occurs when the driving frequency applied to the system matches the natural frequency of the system;

• When this happens, the amplitude of vibrations is then a maximum.

State and explain an everyday example of resonance.

• A child on a swing that is being pushed is an example of resonance:

• In this example, the person pushing provides the driving frequency, and the child on the swing is the part of the system being driven;

• When the driving frequency of the person pushing the swing matches the natural frequency of the swing, the amplitude of oscillations will increase.

Give an example where resonance is a problem.

Earthquakes; the ground vibrating causes buildings to vibrate and possibly collapse.

Explain what is meant by damping.

The loss of energy from the system due to a force which always opposes motion.

State the effects of damping on resonance.

• Smaller amplitude of vibrations;

• The system will have a lower natural frequency (so driving frequency must change in order to produce resonance).