Use the text book or internet to get adefinition for “free and forced vibrations”
Now use a ruler or hack saw bladeconnected to the desk leg, with a paintbrush secured to one end, to draw a traceof a free vibration as the ruler oscillates.Slowly pull the paper along underneath theruler.
Your sheet shouldlook like this whenyou are done
Now plot yourgraph usingreadings takenfrom yourplot/trace
Plot a graph of Amplitude against time(number ofwaves) - the idea being that we can show theexponential decay of the wave amplitude as timegoes on.
S.H.M. using angle sensor and easy sense
Free vibrations decaying over along period of time.
Work through proving that the decay is exponential- To do this Plot log(amplitude) vs log(Time). Iftrue this is a straight line!
POWER LAWNow make some notes to explain plotting graphsusing logs and the “POWER LAW”.
Investigating ForcedVibrationsInvestigating ForcedVibrations
You are going to look at linked pendula, concentratingon the transfer of energy and the phase differencebetween the swinging motion of the system.
Try varying the length of the pendula, one at a timeand observe how the effects differ - can you explainyour observations?
You should write up in the lesson what is happening .
Makeobservations onthe transfer ofenergy and thephasedifferencebetween the twopendula.
Vary the length of the pendula, one at a time andobserve how the effects differ - can you explain yourobservations?
Now observe this system and try to explain theeffects you are seeing!
Pendulamounted onstring to assistenergytransfer!
Now investigate the previous experiment but this timerecording the measurement for the maximum amplitudeof oscillation for the “driven” pendulum and thefrequency of the “driver” by changing the length ofthe driver.
Now plot a graph,using your results, ofDriven Amplitudeagainst DriverFrequency
Investigating ForcedVibrations in springsInvestigating ForcedVibrations in springs
Vibrator
Vibrator moves up and downcausing the spring to oscillate.Observe what happens as thedriving frequency changes
Investigating ForcedVibrations in springsInvestigating ForcedVibrations in springs
driver frequencydriven amplitude400 gUsing the same idea as for the pendulum you should now investigatethe relationship between driver frequency and driven amplitude (keep400 g on the driven)for a pair of oscillating springs hung from aloosely suspended ruler.
Why is the rule loosely suspended?????????
Vary massto changefrequency
Plot the same graphs as forthe pendulum
ResonanceResonance
If you remember seeing thisexperiment you should have seen thetwo pendula with identical lengthsoscillating the most.
In this second experiment it was obvious whenresonance occurred. The mass vibrated such thatit was eventually out of control when the drivingfrequency of the oscillator was at the naturalfrequency of the system. This gives us ourdefinition of resonance……
Resonance: occurs when the driving frequency isequal to the natural frequency of the system it isforcing to vibrate.Resonance: occurs when the driving frequency isequal to the natural frequency of the system it isforcing to vibrate.
In this case the amplitude ofoscillations will build up, to , untilthe system cannot cope and may fallapart e.g Tacoma narrows!!
In this case wecan see theamplitudeincreases rapidlyas the frequencyof the driver isthe same as thatof the drivensystem
Naturalfrequency fo
Amplitude ofvibrations
DrivingFrequency
The amplitude of any natural vibration willgradually decrease.
This process is called DAMPING.
For example, the amplitude of vibration of asimple pendulum decreases because of airresistance and friction at the support. This isan example of natural damping. Many systemsare artificially damped to cut down unwantedvibration - the shock absorbers on a car servethis purpose.
Note that the frequency of the oscillation doesnot change throughout the damping process.
Free vibrations decaying over along period of time.
Effects of dampingEffects of damping
fo
Amplitude of vibrations
Driving Frequency
Increasing levels ofdampingIncreasing levels ofdamping
There are 3 basic damping conditions you need to beaware of:
Underdamped - a small amount of damping which means that thesystem take a long time to settle. This would be the case in asimple pendulum where the only damping is supplied by thefriction in the system due to air resistance and the bearings.
Critically damped - the displacement returns to the equilibriumposition within a quarter of a cycle without going past theequilibrium position - eg a good car shock absorber.
Overdamped - so much damping is applied that thesystem takes a great deal of time to reach theequilibrium position.
These effects can be seen to great effect in thefollowing graph.
Time
Equilibriumposition
Displacement
Over-damped - slowly gets backto normal position
Under-damped oscillationscontinue too long
Critically Damped -returns to normalquickly
SOME CONSEQUENCES OF RESONANCE
•Soldiers need to break step when crossing bridges. (Failure todo so caused the loss of over two hundred Frenchinfantrymen in 1850.)
•Singers can shatter wine glasses by forcing them to vibrateat their natural frequencies.
•A diver on a springboard builds up the amplitude of oscillationof the board by `bouncing' on it at its natural frequency.
•If a loose part in a car rattles when the car is travelling at acertain speed, it is likely that a resonant vibration isoccurring.
•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 controlclocks and watches.