A-level Physics Paper 1: Periodic Motion

Term for how far an object has rotated

Angular displacement

Angular velocity

Rate of angular rotation

What is centripetal acceleration

The acceleration towards the centre of the circle during circular motion

How does centripetal force relate to circular motion

Centripetal force is what causes something to accelerate and change direction in a circular path

What to do when calculating circular motion

Make sure to draw a free body force diagram and calculate resultant forces

Period in SHM

Time taken for one complete oscillation

Frequency in SHM

Number of oscillations per second

Displacement in SHM

The distance from equilibrium

Amplitude in SHM

The maximum displacement

Free oscillation in SHM

No energy is lost to the surroundings, and oscillation is not damped

How do velocity and displacement relate in SHM

There is a phase difference of π/2

For a cart moving backwards and forwards between two springs, with no damping, what happens to energy over time

Kinetic energy and elastic potential energy sum to a constant; E_k goes up as E_p goes down, and vice versa. E_k is max at equilibrium point, E_p is max at amplitude point

What happens to energy in damping

Some of it is lost such as via heat energy

Light damping in SHM

Time period independent of amplitude, so cycle takes same time as oscillations amplitude decreases exponentially over time

Critical damping in SHM

Stops oscillations quickly after released after being displaced from equilibrium, with no overshooting

Heavy damping

A slow critical damping with no further oscillating motion

What's special about the natural frequency in SHM

It's the frequency at which free oscillations occur

Examples of forced vibrations in mechanical systems (3)

Bridges swaying as people walk on them, stationary waves on strings, glass shattering at a certain frequency

Forced vibrations in SHM

When a system oscillates with a periodic force being applied

Resonance

When the driving oscillator frequency matches the natural frequency of the system

Why must the frequency of the periodic force equal the natural frequency in order to cause resonance

To have a constant phase relationship of π/2

For the graph of amplitude versus frequency, what happens as you lighten the damping

the maximum amplitude at resonance becomes larger, and the resonant frequency gets closer (to the right) to the natural frequency of the system, and the peak becomes sharper

What happens as you increase the damping for a graph of amplitude versus frequency

Lower max amplitude and frequency (to the left) due to damping; broader peaks due to energy loss from damping

Requirement for a pendulum to be SHM

Small angle θ<10 so sin(θ)≈θ

Application of damping in the real world

Light damping is used to minimise effects of earthquakes; Critical damping is used for car suspension to avoid bouncing

How does acceleration relate to displacement in SHM

It is directly proportional to displacement, and directed towards the equilibrium position; α is proportional to -x

What is ω in SHM

The phase change per second, where 2π rad is one full oscillation