Topic 5.3 - Oscillations

Front 1

SHM definition

Back 1

An oscillation in which the acceleration of an object is directly proportional to its displacement from the midpoint (equilibrium position), and is directed towards the midpoint

Front 2

Amplitude

Back 2

maximum displacement from the midpoint

Front 3

Kinetic + Potential Energy

Back 3

Mechanical Energy - stays constant if undamped

Front 4

Cycle of Oscillation

Back 4

maximum positive displacement to maximum negative displacement and back again

Front 5

Force on spring

Back 5

F = -kx

k: spring constant

Front 6

Period of mass oscillating on a spring

Back 6

T = 2π √(m / k)

k: spring constant

Front 7

Investigating the Mass-Spring System (Setup)

Back 7

- Trolley attached between 2 springs, one joined to a fixed point and the other to a force meter and data logger

- I/\/\/\/\/\/-(Trolley)-/\/\/\/\/\/\I----(Data logger)

- Data logger draws displacement-time graph to show T

Front 8

Investigating the Mass-Spring System (Method)

Back 8

- Pull to one side by certain amount & let go

- Change mass by loading trolley with masses (include mass of trolley in calculations)

- Change k with different spring combinations

- Change A by pulling across different amounts

Front 9

Investigating the Mass-Spring System (Results)

Back 9

- T ∝ √m -so- T^2 ∝ m

- T ∝ √(1/k) -so- T^2 ∝ 1/k

- T doesn't depend on A

Front 10

Period of pendulum

Back 10

T = 2π √(l / g)

l: distance between pivot & centre of mass of the bob

Front 11

Free Vibrations

Back 11

- Oscillates at natural frequency and no energy transferred to the surroundings

- Never happens, but in air vibrations caused free

Front 12

Driving Frequency

Back 12

Frequency of periodic external force causing a system to vibrate

Front 13

Resonance

Back 13

Driving frequency = natural frequency

As driving frequency approaches natural frequency system gains more and more energy vibrates with rapidly increasing amplitude

Front 14

Resonance examples

Back 14

Organ Pipe - Column of air resonates, driven by motion of air at the base

Swing - Resonates when someone pushes it at its natural frequency

Glass Smashing - When driven by sound wave at right frequency

Radio - Tuned so electric current resonates at same frequency as the desired radio station

Front 15

Damping Forces

Back 15

Force that causes oscillating system to lose energy (usually frictional / air resistance)

Systems often deliberately damped to reduce resonance

Car shock absorbers damp by squashing oil through a small hole when compressed

Front 16

Damping & Amplitude / Frequency

Back 16

Damping reduces the amplitude of the oscillation over time and reduces the frequency by a set amount

Front 17

Critical Damping

Back 17

Stops oscillations in the shortest possible time as the two forces balance eachother

Car suspension & loud speakers are critically damped so they don't oscillate

Front 18

Overdamping

Back 18

Heavier damping than critical damping. Damping overwrites spring and prevents it from reaching rest position. It approaches equilibrium. No oscillation

Door damping / non-slam

Front 19

Underdamping

Back 19

Amplitude decreases over time but does not reach zero (musical instruments)

Front 20

Lightly Damped Resonance Peak

Back 20

Very sharp. Amplitude only increases dramatically when driving frequency very close to natural frequency

Front 21

Heavily Damped Resonance Peak

Back 21

Flatter. Amplitude doesn't increase so much close to natural frequency and is less sensitive to the driving frequency

Front 22

Natural Frequency

Back 22

The frequency at which a system will vibrate freely

Front 23

Periodic motion

Back 23

The regular, repetitive motion of a body which continually retraces its path at regular intervals

Front 24

Damping

Back 24

The process whereby energy is taken from the oscillating system