11: Modelling Oscillations Flashcards
Define simple harmonic motion
An oscillation in which the restoring force on an object, and hence the acceleration of the object, is directly proportional to its displacement from the midpoint, and is directed towards the midpoint
What is the type of potential energy that is providing the restoring force for pendulums?
Gravitational
What is the type of potential energy that is providing the restoring force for springs?
Elastic strain energy
Describe the different energies as the object moves towards the midpoint and away again
(Simple harmonic motion)
As the object moves towards the midpoint, the restoring force does work on the object and so transfers some PE to KE
When the object is moving away from the midpoint, all that KE is transferred back to PE again.
What is the potential energy and the kinetic energy, when the object is at the midpoint?
(Simple harmonic motion)
PE = 0 KE = maxiumum
What is the potential energy and the kinetic energy, when the object is at the maximum displacement?
(Simple harmonic motion)
KE = 0 PE = maximum
Describe the sum of the potential and kinetic energy of an object in simple harmonic motion
The mechanical energy stays constant
Mechanical energy = KE + PE
What is the cycle of an oscillation?
From maximum positive displacement to maximum negative displacement and back again
Describe the relationship between frequency, period, and amplitude and simple harmonic motion
The frequency and period are independent of the amplitude
Describe the set up for the experiment of a mass on a spring in simple harmonic motion
A mass on the end of the spring connected to a string, held in a clamp and clamp stand on the edge of a workbench. Underneath the mass is a position sensor, attached to a computer
Describe the experiment of a mass on the end of the spring
SHM
Pull the masses down a set amount – this displacement will be your initial amplitude. Let the masses go
The masses will now oscillate with simple harmonic motion.
The position sensor will measure the displacement of the mass over time
Create a displacement time graph. Read off the time period
Experiment looking at a mass on the end of a spring, (SHM):
How can you investigate how mass changes the experiment?
Add extra masses to the spring
Don’t stretch the spring past its limit of proportionality
Experiment looking at a mass on the end of a spring, (SHM):
How can you investigate how the spring constant changes the experiment?
Use different springs, or combinations of springs.
Experiment looking at a mass on the end of a spring, (SHM):
How can you investigate how amplitude changes the experiment?
Pull the mass down by different amounts. Be careful about how far you stretch the spring, don’t stretch it past the limit of proportionality
Describe the set up of the investigation of a simple pendulum
Attach a piece of card and a protractor to a clamp on a clampstand. Attach a string with a bob on the end to the clamp. Put a reference mark in the equilibrium position
Measure the mass of the bob and use a ruler to find the length of the string
Describe the investigation of the simple pendulum
Pull the bob to the side and measure the angle between the string and the vertical. Position your eyelevel with the reference mark then let the bob go. Start the stopwatch when the bob passes in front of the mark, then record the times when the bob passes in front of the mark again, travelling from the same direction. The length of the time the elapses between each time the bob passes in front of the mark from the same direction is the time period.
Investigation of the simple pendulum: how can you make the calculation of the time period more accurate?
T might be too short to measure accurately from one swing. If so, measure the total time for a number of complete oscillations combined and divide this time by the number of oscillations to find the time period
The investigation of the simple pendulum only works with [ ] angles
Small
Less than 10°
What is a free vibration?
When something oscillates at its natural frequency. If no energy is transferred to or from the surroundings, it will keep oscillating with the same amplitude forever.
Describe resonance
When the driving frequency approaches the natural frequency, the system gains more and more energy from the driving force and so vibrates with a rapidly increasing amplitude
Resonance: driving frequency = natural frequency
What are forced vibrations?
Vibrations produced when a system is forced to vibrate by a periodic external force
What is the driving frequency?
The frequency of the periodic external force which results in forced vibrations
What are damping forces?
Forces that cause any oscillating system to lose energy to its surroundings
Why are systems often deliberately damped?
To stop the oscillating or to minimise the effect of resonance
What does damping do?
Reduces the amplitude of the oscillation over time. The heavier the damping, the quicker the amplitude is reduced to 0
What is critical damping?
It reduces the amplitude in the shortest possible time – it stops the system oscillating
How is plastic deformation linked to damping?
Plastic deformation of ductile materials reduces the amplitude of oscillations in the same way as damping. As the material changes shape, it absorbs energy, so the oscillation will become smaller
Which will take longer to return to equilibrium, and overdamped system, or a critically damped system?
Overdamped
Describe the difference between light damping and heavy damping on a graph of displacement against time
Both are distorted cosine waves. The more heavily damped one reduces in amplitude quickly as time increases
Describe the graph of displacement against time for critical damping
Displacement starts at maximum then extremely quickly decreases to 0
Describe the graph of displacement against time for overdamping
Displacement starts off high and gradually reduces to 0 over a longer period of time (than critical damping)
Describe resonance, if the system is lightly damped
Lightly damped systems have a very sharp resonance peak. Their amplitude only increases dramatically when the driving frequency is very close to the natural frequency
Describe resonance, if the system is heavily damped
Heavily damped systems have a flatter response. The amplitude doesn’t increase very much near the natural frequency, and they aren’t as sensitive to the driving frequency
Describe the set up for the investigation of how amplitude varies with driving frequency
(SHM)
Put a mass between two springs, one attached to a clamp, the other attached to a vibration generator, which in turn is connected to a signal generator, which sets the driving frequency
Describe how to investigate how amplitude varies with driving frequency
(SHM)
If you vary the driving frequency using the signal generator, and plot amplitude against driving frequency you get a graph. The natural frequency is where there is maximum amplitude
Explain the set up for the investigation of how damping affects resonance
(SHM)
Put a mass between two springs, one attached to a clamp, the other attached to a vibration generator which in turn is connected to a signal generator
Add a disc between the mass, and the spring that is attached to the vibration generator
Describe the investigation of how damping affects resonance
SHM
The mass oscillates at a smaller amplitude at the resonant frequency than a free oscillator
Adding a disc increases air resistance
In general, the more damped a system is, the flatter the graph of amplitude of oscillation against driving frequency
