Use the text book or internet to get a definition for “free and forced vibrations” Now use a ruler or hack saw blade connected to the desk leg, with a paint brush secured to one end, to draw a trace of a free vibration as the ruler oscillates. Slowly pull the paper along underneath the ruler.

Your sheet should look like this when you are done Now plot your graph using readings taken from your plot/trace Plot a graph of Amplitude against time(number of waves) - the idea being that we can show the exponential decay of the wave amplitude as time goes on.

S.H.M. using angle sensor and easy sense

Free vibrations decaying over a long period of time. Work through proving that the decay is exponential - To do this Plot log(amplitude) vs log(Time). If true this is a straight line! POWER LAW Now make some notes to explain plotting graphs using logs and the “POWER LAW”.

Investigating Forced Vibrations You are going to look at linked pendula, concentrating on the transfer of energy and the phase difference between the swinging motion of the system. Try varying the length of the pendula, one at a time and observe how the effects differ - can you explain your observations? You should write up in the lesson what is happening.

Make observations on the transfer of energy and the phase difference between the two pendula. Vary the length of the pendula, one at a time and observe how the effects differ - can you explain your observations?

Now observe this system and try to explain the effects you are seeing! Pendula mounted on string to assist energy transfer!

Now investigate the previous experiment but this time recording the measurement for the maximum amplitude of oscillation for the “driven” pendulum and the frequency of the “driver” by changing the length of the driver. Now plot a graph, using your results, of Driven Amplitude against Driver Frequency

Investigating Forced Vibrations in springs Vibrator Vibrator moves up and down causing the spring to oscillate. Observe what happens as the driving frequency changes

Investigating Forced Vibrations in springs driver frequencydriven amplitude 400 g Using the same idea as for the pendulum you should now investigate the relationship between driver frequency and driven amplitude (keep 400 g on the driven)for a pair of oscillating springs hung from a loosely suspended ruler. Why is the rule loosely suspended????????? Vary mass to change frequency Plot the same graphs as for the pendulum

Resonance If you remember seeing this experiment you should have seen the two pendula with identical lengths oscillating the most. In this second experiment it was obvious when resonance occurred. The mass vibrated such that it was eventually out of control when the driving frequency of the oscillator was at the natural frequency of the system. This gives us our definition of resonance……

Resonance: occurs when the driving frequency is equal to the natural frequency of the system it is forcing to vibrate.  In this case the amplitude of oscillations will build up, to , until the system cannot cope and may fall apart e.g Tacoma narrows!!

In this case we can see the amplitude increases rapidly as the frequency of the driver is the same as that of the driven system Natural frequency f o Amplitude of vibrations Driving Frequency

The amplitude of any natural vibration will gradually decrease. This process is called DAMPING. For example, the amplitude of vibration of a simple pendulum decreases because of air resistance and friction at the support. This is an example of natural damping. Many systems are artificially damped to cut down unwanted vibration - the shock absorbers on a car serve this purpose. Note that the frequency of the oscillation does not change throughout the damping process.

Free vibrations decaying over a long period of time. Effects of damping

fofo Amplitude of vibrations Driving Frequency Increasing levels of damping

There are 3 basic damping conditions you need to be aware of: Underdamped - a small amount of damping which means that the system take a long time to settle. This would be the case in a simple pendulum where the only damping is supplied by the friction in the system due to air resistance and the bearings. Critically damped - the displacement returns to the equilibrium position within a quarter of a cycle without going past the equilibrium position - eg a good car shock absorber. Overdamped - so much damping is applied that the system takes a great deal of time to reach the equilibrium position.

These effects can be seen to great effect in the following graph. Time Equilibrium position Displacement Over-damped - slowly gets back to normal position Under-damped oscillations continue too long Critically Damped - returns to normal quickly

SOME CONSEQUENCES OF RESONANCE Soldiers need to break step when crossing bridges. (Failure to do so caused the loss of over two hundred French infantrymen in 1850.) Singers can shatter wine glasses by forcing them to vibrate at their natural frequencies. A diver on a springboard builds up the amplitude of oscillation of the board by `bouncing' on it at its natural frequency. If a loose part in a car rattles when the car is travelling at a certain speed, it is likely that a resonant vibration is occurring. A column of air can be made to resonate to a particular note. Electrical resonance is made use of to tune radio circuits. Resonant vibrations of quartz crystals are used to control clocks and watches. Tacoma Narrows bridge collapseTacoma Narrows