Oscillations

What is displacement in SHM?

Distance from the equilibrium position.

What is amplitude?

Maximum displacement from equilibrium.

What is the period of an oscillation?

Time taken for one full oscillation.

What is frequency?

Number of oscillations per second.

What is the unit of frequency?

Hertz (Hz).

What is the relationship between frequency and period?

f = 1/T.

What is phase difference?

Fraction of an oscillation between two oscillators.

How is phase difference expressed in radians?

Δφ = fraction × 2π.

What is angular frequency?

Rate of change of angular position.

What is the equation for angular frequency?

ω = 2πf.

What is the unit of angular frequency?

Radians per second (rad s⁻¹).

What is simple harmonic motion (SHM)?

Oscillation where acceleration is proportional to displacement and directed towards equilibrium.

What is the SHM acceleration equation?

a = −ω²x.

What does the negative sign in a = −ω²x show?

Acceleration acts towards equilibrium.

What does isochronous mean?

Period is independent of amplitude.

Are SHM oscillations isochronous?

Yes.

How can the period of SHM be measured?

Time several oscillations and divide by the number.

Why time multiple oscillations instead of one?

To reduce percentage uncertainty.

What is a fiducial marker used for?

A fixed reference point for timing.

Where is the fiducial marker usually placed?

At the equilibrium position.

State the displacement equation using sine

x = A sin(ωt).

When is x = A sin(ωt) used?

When motion starts at equilibrium.

State the displacement equation using cosine

x = A cos(ωt).

When is x = A cos(ωt) used?

When motion starts at maximum displacement.

What does A represent in SHM equations?

Amplitude.

What does ω represent in SHM equations?

Angular frequency.

How is velocity found from a displacement–time graph?

Gradient of the graph.

Where is velocity maximum in SHM?

At equilibrium.

Where is velocity zero in SHM?

At maximum displacement.

Where is acceleration maximum in SHM?

At maximum displacement.

Where is acceleration zero in SHM?

At equilibrium.

State the velocity equation for SHM

v = ±ω√(A² − x²).

State the maximum velocity equation

vmax = ωA.

Where does maximum velocity occur?

At equilibrium (x = 0).

What happens to kinetic energy at equilibrium?

It is maximum.

What happens to potential energy at equilibrium?

It is minimum.

Where is potential energy maximum in SHM?

At amplitude.

What happens to kinetic energy at amplitude?

It is zero.

Is total energy conserved in SHM?

Yes.

What forms of energy interchange in SHM?

Kinetic and potential energy.

What is damping?

Reduction in amplitude over time due to energy loss.

What causes damping?

Resistive forces such as friction or air resistance.

What is light damping?

Slow exponential decrease in amplitude.

Give an example of light damping

A pendulum oscillating in air.

What is heavy damping?

Rapid reduction in amplitude.

Give an example of heavy damping

A pendulum oscillating in water.

What is critical damping?

System returns to equilibrium in shortest time without oscillating.

Give an example of critical damping

A pendulum in thick fluid (e.g. treacle).

What is free oscillation?

Oscillation at natural frequency without external force.

What is forced oscillation?

Oscillation due to an external periodic driving force.

What is natural frequency?

Frequency an object oscillates at freely.

What is resonance?

Large amplitude oscillation when driving frequency = natural frequency.

What happens to amplitude at resonance?

It becomes maximum.

What happens if there is no damping at resonance?

Amplitude increases until system failure.

How does damping affect resonance amplitude?

Increased damping reduces peak amplitude.

How does damping affect resonance frequency?

Peak shifts to slightly lower frequency.

How can resonance be investigated experimentally?

Mass–spring system driven by oscillator.

What is varied in a resonance experiment?

Driving frequency.

What is measured in a resonance experiment?

Amplitude of oscillation.

When is amplitude maximum in the experiment?

At natural frequency.

Why film resonance experiments?

To measure amplitude more accurately.