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# 13.1. Mechanical Oscillations

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### 13.1. Mechanical Oscillations

1. 1. Module 4: waves fields and nuclear energy 13.1 oscillations and waves Mechanical oscillations
2. 2. Mechanical oscillations <ul><li>3 common forms of motion: linear, circular and oscillatory </li></ul><ul><li>Examples of oscillatory motion include: </li></ul><ul><li>- the to and fro motion of simple pendulums or masses on vibrating strings </li></ul><ul><li>- the strings and columns of musical instruments when producing a note </li></ul><ul><li>- vibrations in turbines, engines and tall buildings </li></ul>
3. 3. <ul><li>In mechanical oscillations there is a continual interchange of potential and kinetic energy because the system has: </li></ul><ul><ul><li>Elasticity – allowing it to store PE </li></ul></ul><ul><ul><li>Inertia (mass) – allowing it to have KE </li></ul></ul><ul><li>Consider a spring with a mass attached, which is pulled down and released: </li></ul>
4. 4. <ul><li>Elastic restoring force pulls mass up  mass accelerates towards O (velocity increases) </li></ul><ul><li>As mass approaches O, accelerating force decreases  acceleration decreases </li></ul><ul><li>At O, elastic force = 0, but mass has inertia so it carries on moving up </li></ul><ul><li>Spring is now compressed  restoring force acts down </li></ul><ul><li>Mass slows down (acceleration reduced) and rests at B </li></ul>
5. 5. <ul><li>Motion is then repeated in opposite direction </li></ul><ul><li>PE stored as elastic energy of the spring is continually changed to KE of the moving mass and vice versa </li></ul>
6. 6. <ul><li>Motion would continue indefinitely if no energy loss occurred. </li></ul><ul><li>Energy is lost. Why? </li></ul>
7. 7. <ul><li>Real oscillatory objects transfer energy to the surroundings as friction or air resistance. </li></ul><ul><li>The amplitude (or displacement) of the object gets less with time. </li></ul><ul><li>These are damped oscillations. </li></ul>
8. 8. Time period, frequency and displacement <ul><li>Time taken for a complete oscillation from A to O to B and back to A is called the Time period, T </li></ul><ul><li>Frequency, f is number of compete oscillations per unit time (usually 1 second) </li></ul><ul><li>f = 1 or T = 1 </li></ul><ul><li> T f </li></ul>
9. 9. <ul><li>Displacement ( x ) is the distance from equilibrium. </li></ul><ul><li>a.k.a. the amplitude of the oscillation </li></ul><ul><li>Displacement = distance OA or OB </li></ul><ul><li>Restoring force increases with displacement, but acts in the opposite direction (always toward equilibrium) </li></ul><ul><li>F  - x </li></ul>
10. 10. Simple oscillatory systems <ul><li>Try and discover experimentally : </li></ul><ul><li>(i) which of the following systems have constant time period </li></ul><ul><li>(ii) what factors determine the time period or frequency of the oscillation </li></ul><ul><li>What is a reliable method of measuring T? </li></ul>
11. 11. (f)
12. 12. Graphical representation of oscillations <ul><li>Simple oscillations are shown in displacement-time graphs or time traces </li></ul><ul><li>These can be obtained using DL+ and computer software (none of our computers are compatible, however!!) </li></ul>
13. 13. <ul><li>Amplitude of wave = displacement from equilibrium </li></ul><ul><li>Wavelength = time period </li></ul>
14. 14. Questions <ul><li>(a) What is the period of a 50Hz oscillation? </li></ul><ul><li>(b) What is the frequency of a swing that moves from one extreme to the centre of its motion in 0.7s? </li></ul><ul><li>(c) What is the fundamental (lowest) frequency of the guitar note below? </li></ul>
15. 15. <ul><li>Look at the diagram below. </li></ul><ul><li>(a) Sketch a graph for one cycle of the swings motion and label the points A-E. </li></ul><ul><li>(b) Where does the swing have maximum velocity, maximum KE, maximum GPE, maximum acceleration and zero velocity? </li></ul><ul><li>(c) If no-one pushes the swing it will stop swinging. Why? </li></ul>
16. 16. <ul><li>Sketch displacement-time graphs for the following examples and suggest suitable values for the amplitude and frequency in each case. </li></ul><ul><li>(a) Your arm swinging freely as you walk (use angular displacement). </li></ul><ul><li>(b) a perfectly elastic ball bouncing vertically on a rigid solid surface. </li></ul><ul><li>(c) The free end of a plastic ruler held over the edge of the table, bent downwards and released to vibrate vertically. </li></ul>