PHYSICS MODULE 5.3 OSCILLATIONS

SELF EXPLANATORY

Define displacement in oscillations.

Displacement, x, is the distance and direction of an object from its equilibrium position.

It is a vector quantity.

The equilibrium position is where the resultant force is zero.

Define amplitude.

Amplitude, AAA, is the maximum displacement from the equilibrium position.

It is always a positive value.

Define period.

The period, TTT, is the time taken for one complete oscillation.

Define frequency.

Frequency, fff, is the number of complete oscillations per second.

f=1/T

Define angular frequency.

Angular frequency, ω\omegaω, is the rate of change of phase angle.

Unit:

rads^−1

Equation:

ω=2πf

Define phase difference.

Phase difference is the fraction of a cycle by which one oscillation leads or lags another.

It can be measured in:

• radians

• degrees

• fraction of a cycle

Equation:

ϕ=2πΔt/T

Define simple harmonic motion (SHM).

Simple harmonic motion is motion where:

acceleration is directly proportional to displacement from equilibrium and acts towards the equilibrium position.

Equation:

a=−ω^2x

The negative sign shows acceleration is always opposite to displacement.

Why is the minus sign important in the SHM equation?

The minus sign shows that the acceleration is always directed towards the equilibrium position, while the displacement is away from equilibrium.

This means:

• if displacement is positive, acceleration is negative

• if displacement is negative, acceleration is positive

So acceleration and displacement are always in opposite directions.

This restoring acceleration is what causes the object to oscillate back and forth.

State the displacement equations for SHM.

If motion starts at equilibrium:

x=Asin⁡(ωt)

If motion starts at maximum displacement:

x=Acos⁡(ωt)

You must identify the starting position first.

State the velocity equation for SHM.

^^^^^^^^^^^______

V= +-ROOT/ A²-W²

Maximum velocity occurs at equilibrium where:

x=0

so:

vmax=Aω

Where are maximum velocity and maximum acceleration in SHM?

Maximum velocity:

• at equilibrium position

• where displacement = 0

Maximum acceleration:

• at maximum displacement

• at amplitude positions

At equilibrium:

• acceleration = 0

At amplitude:

• velocity = 0

Why is SHM called isochronous?

Because the period is independent of amplitude.

This means:

even if amplitude changes, the time for one oscillation stays the same.

An oscillator with this property is called an isochronous oscillator.

Required Practical (PAG): How is the period of SHM measured?

Examples:

• pendulum

• mass on a spring

Method:

• displace the object slightly

• release it

• use a fiducial marker at equilibrium position

• time several oscillations (usually 10+)

• divide total time by number of oscillations

This improves accuracy.

Then:F=1/T

Why should small amplitudes be used in SHM practicals?

Because large amplitudes may cause the motion to stop being simple harmonic.

Especially for pendulums:

large angles mean motion is no longer a good SHM approximation.

Small amplitudes improve accuracy.

Describe energy changes during SHM.

Energy constantly transfers between:

• kinetic energy (KE)

• potential energy (PE)

Total energy remains constant if there is no damping.

At equilibrium:

• KE is maximum

• PE is minimum

At maximum displacement:

• KE is zero

• PE is maximum

Describe the energy-displacement graph for SHM.

Total energy:

• constant horizontal line

Kinetic energy:

• maximum at equilibrium

• zero at amplitude

Potential energy:

• minimum at equilibrium

• maximum at amplitude

KE + PE = constant total energy

What is damping?

Damping is the removal of energy from an oscillating system, causing amplitude to decrease over time.

It is caused by resistive forces such as:

• friction

• air resistance

• drag

Describe light damping, heavy damping and critical damping.

Light damping:

• amplitude gradually decreases

• oscillations continue

Heavy damping:

• amplitude decreases quickly

• few or no oscillations

Critical damping:

• system returns to equilibrium in shortest possible time without oscillating

Examples:

car suspension systems use critical damping

Define free oscillations.

Free oscillations happen when a system oscillates at its natural frequency with no external driving force.

The system is left alone after being disturbed

Define forced oscillations.

Forced oscillations happen when an external periodic driving force makes the system oscillate.

The system oscillates at the driving frequency.

Define natural frequency.

Natural frequency is the frequency at which a system oscillates when no external driving force acts.

Every oscillating system has its own natural frequency.

Define resonance.

Resonance is when the driving frequency of a forced oscillation equals the natural frequency of the system, causing maximum energy transfer and maximum amplitude of oscillation.

Describe the amplitude-frequency graph for resonance.

At resonance:

• amplitude reaches a maximum peak

With more damping:

• peak becomes lower

• peak becomes wider

• resonant frequency shifts slightly lower

Give examples of resonance in real life.

Useful:

• tuning a radio

• musical instruments

Dangerous:

• bridges collapsing

• buildings shaking in earthquakes

• glass shattering

Give two practical examples of forced oscillations.

Child on a swing: pushes provide the driving force and force the swing to oscillate.

Buildings in earthquakes
Seismic waves provide a driving force. Buildings are forced to oscillate due to ground motion.

Give two practical examples of resonance.

• Radio tuning: when driving frequency matches natural frequency, amplitude becomes maximum and one station is selected.

• Bridges: if wind or marching matches the natural frequency, very large oscillations can occur and may cause collapse.