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13.1. Mechanical Oscillations
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Transcript of 13.1. Mechanical Oscillations
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Module 4: waves fields and nuclear energy
13.1 oscillations and waves
Mechanical oscillations
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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
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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:
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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
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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
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Motion would continue indefinitely if no energy loss occurred.
Energy is lost. Why?
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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.
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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
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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
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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?
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(f)
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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!!)
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Amplitude of wave = displacement from equilibrium
Wavelength = time period
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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?
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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?
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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.