11: Modelling Oscillations

Question 1

Define simple harmonic motion

Answer 1

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

Question 2

What is the type of potential energy that is providing the restoring force for pendulums?

Answer 2

Gravitational

Question 3

What is the type of potential energy that is providing the restoring force for springs?

Answer 3

Elastic strain energy

Question 4

Describe the different energies as the object moves towards the midpoint and away again
(Simple harmonic motion)

Answer 4

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.

Question 5

What is the potential energy and the kinetic energy, when the object is at the midpoint?
(Simple harmonic motion)

Answer 5

PE = 0
KE = maxiumum

Question 6

What is the potential energy and the kinetic energy, when the object is at the maximum displacement?
(Simple harmonic motion)

Answer 6

KE = 0
PE = maximum

Question 7

Describe the sum of the potential and kinetic energy of an object in simple harmonic motion

Answer 7

The mechanical energy stays constant

Mechanical energy = KE + PE

Question 8

What is the cycle of an oscillation?

Answer 8

From maximum positive displacement to maximum negative displacement and back again

Question 9

Describe the relationship between frequency, period, and amplitude and simple harmonic motion

Answer 9

The frequency and period are independent of the amplitude

Question 10

Describe the set up for the experiment of a mass on a spring in simple harmonic motion

Answer 10

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

Question 11

Describe the experiment of a mass on the end of the spring

SHM

Answer 11

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

Question 12

Experiment looking at a mass on the end of a spring, (SHM):

How can you investigate how mass changes the experiment?

Answer 12

Add extra masses to the spring

Don’t stretch the spring past its limit of proportionality

Question 13

Experiment looking at a mass on the end of a spring, (SHM):

How can you investigate how the spring constant changes the experiment?

Answer 13

Use different springs, or combinations of springs.

Question 14

Experiment looking at a mass on the end of a spring, (SHM):

How can you investigate how amplitude changes the experiment?

Answer 14

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

Question 15

Describe the set up of the investigation of a simple pendulum

Answer 15

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

Question 16

Describe the investigation of the simple pendulum

Answer 16

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.

Question 17

Investigation of the simple pendulum: how can you make the calculation of the time period more accurate?

Answer 17

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

Question 18

The investigation of the simple pendulum only works with [ ] angles

Answer 18

Small

Less than 10°

Question 19

What is a free vibration?

Answer 19

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.

Question 20

Describe resonance

Answer 20

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

Question 21

What are forced vibrations?

Answer 21

Vibrations produced when a system is forced to vibrate by a periodic external force

Question 22

What is the driving frequency?

Answer 22

The frequency of the periodic external force which results in forced vibrations

Question 23

What are damping forces?

Answer 23

Forces that cause any oscillating system to lose energy to its surroundings

Question 24

Why are systems often deliberately damped?

Answer 24

To stop the oscillating or to minimise the effect of resonance

Question 25

What does damping do?

Answer 25

Reduces the amplitude of the oscillation over time. The heavier the damping, the quicker the amplitude is reduced to 0

Question 26

What is critical damping?

Answer 26

It reduces the amplitude in the shortest possible time – it stops the system oscillating

Question 27

How is plastic deformation linked to damping?

Answer 27

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

Question 28

Which will take longer to return to equilibrium, and overdamped system, or a critically damped system?

Answer 28

Overdamped

Question 29

Describe the difference between light damping and heavy damping on a graph of displacement against time

Answer 29

Both are distorted cosine waves. The more heavily damped one reduces in amplitude quickly as time increases

Question 30

Describe the graph of displacement against time for critical damping

Answer 30

Displacement starts at maximum then extremely quickly decreases to 0

Question 31

Describe the graph of displacement against time for overdamping

Answer 31

Displacement starts off high and gradually reduces to 0 over a longer period of time (than critical damping)

Question 32

Describe resonance, if the system is lightly damped

Answer 32

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

Question 33

Describe resonance, if the system is heavily damped

Answer 33

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

Question 34

Describe the set up for the investigation of how amplitude varies with driving frequency
(SHM)

Answer 34

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

Question 35

Describe how to investigate how amplitude varies with driving frequency
(SHM)

Answer 35

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

Question 36

Explain the set up for the investigation of how damping affects resonance
(SHM)

Answer 36

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

Question 37

Describe the investigation of how damping affects resonance

SHM

Answer 37

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