Module 4: waves fields and nuclear energy

13.1 oscillations and waves

Mechanical oscillations

Mechanical oscillations

3 common forms of motion: linear, circular and oscillatory

Examples of oscillatory motion include:- the to and fro motion of simple pendulums or masses on vibrating strings- the strings and columns of musical

instruments when producing a note- vibrations in turbines, engines and tall

buildings

In mechanical oscillations there is a continual interchange of potential and kinetic energy because the system has:

Elasticity – allowing it to store PE Inertia (mass) – allowing it to have KE

Consider a spring with a mass attached, which is pulled down and released:

Elastic restoring force pulls mass up mass accelerates towards O (velocity increases)

As mass approaches O, accelerating force decreases acceleration decreases

At O, elastic force = 0, but mass has inertia so it carries on moving up

Spring is now compressed restoring force acts down

Mass slows down (acceleration reduced) and rests at B

Motion is then repeated in opposite direction

PE stored as elastic energy of the spring is continually changed to KE of the moving mass and vice versa

Motion would continue indefinitely if no energy loss occurred.

Energy is lost. Why?

Real oscillatory objects transfer energy to the surroundings as friction or air resistance.

The amplitude (or displacement) of the object gets less with time.

These are damped oscillations.

Time period, frequency and displacement

Time taken for a complete oscillation from A to O to B and back to A is called the Time period, T

Frequency, f is number of compete oscillations per unit time (usually 1 second)

f = 1 or T = 1

T f

Displacement (x) is the distance from equilibrium.

a.k.a. the amplitude of the oscillation Displacement = distance OA or OB Restoring force increases with

displacement, but acts in the opposite direction (always toward equilibrium)

F - x

Simple oscillatory systems

Try and discover experimentally :

(i) which of the following systems have constant time period

(ii) what factors determine the time period or frequency of the oscillation

What is a reliable method of measuring T?

(f)

Graphical representation of oscillations

Simple oscillations are shown in displacement-time graphs or time traces

These can be obtained using DL+ and computer software (none of our computers are compatible, however!!)

Amplitude of wave = displacement from equilibrium

Wavelength = time period

Questions

1. (a) What is the period of a 50Hz oscillation?

(b) What is the frequency of a swing that moves from one extreme to the centre of its motion in 0.7s?

(c) What is the fundamental (lowest) frequency of the guitar note below?

2. Look at the diagram below.

(a) Sketch a graph for one cycle of the swings motion and label the points A-E.

(b) Where does the swing have maximum velocity, maximum KE, maximum GPE, maximum acceleration and zero velocity?

(c) If no-one pushes the swing it will stop swinging. Why?

3. Sketch displacement-time graphs for the following examples and suggest suitable values for the amplitude and frequency in each case.

(a) Your arm swinging freely as you walk (use angular displacement).

(b) a perfectly elastic ball bouncing vertically on a rigid solid surface.

(c) The free end of a plastic ruler held over the edge of the table, bent downwards and released to vibrate vertically.