Further Mechanics FM06-11

Question 1

Define the symbols that are used in formulas: x, v, a, A, t, T, wierd w?

Answer 1

Displacement
Velocity
Acceleration
Amplitude
time
Time period
Angular speed

Question 2

What is the Time period?

Answer 2

The time taken for one complete oscillation.

Question 3

What is a free oscillation?

Answer 3

Occurs when there is an absence of friction and must have a constant amplitude.

Question 4

What is a driven (forced) oscillation?

Answer 4

An external driving force is being added to the system, causing the amplitude to be different, but still SHM.

Question 5

What is Resonance?

Answer 5

It is characterised by large amplitude oscillations.
It occurs when the frequency of a periodic driving force = natural frequency of the driven object if no/light damping is present.
The amplitude at resonance depends on the degree of damping present.
A phase difference between the driver and driven oscillator is pi/2.

Question 6

What is damping?

Answer 6

Resistive forces are present.
They appose the motion and remove energy from the system.
This causes the amplitude of the oscillations to decrease with time.

Question 7

For the graph of damping: What does the Undamped graph look like?

Answer 7

Total energy is conserved, the same.

Question 8

For the graph of damping: What does the Light damping graph look like?

Answer 8

settles at equlibrium after oscillating many times, e.g. pendulum on the air.

Question 9

For the graph of damping: What does the Critically damped graph look like?

Answer 9

settles at equilibrium in the shortest time, e.g. car suspension.

Question 10

For the graph of damping: What does the Overdamped graph look like?

Answer 10

settles at equilibrium slowly.

Question 11

Describe what the formula a = -ω2x means?

Answer 11

The acceleration is the angular speed squared times the negative displacement.
This is because the acceleration is directly proportional to the negative displacement.

Question 12

What can we say about the time period of a simple harmonic oscillator?

Answer 12

It is independent of amplitude for an object moving with SHM.

Question 13

Describe what happens to an oscillator when the driving frequency is slowly increased from 0Hz.

Answer 13

A graph of driving frequency f against amplitude A of oscillations is called a resonance curve. It has the following key features:
When f < f0, the amplitude of oscillations increases.
At the peak where f = f0, the amplitude is at its maximum. This is resonance
When f > f0, the amplitude of oscillations starts to decrease.

Question 14

What is frequency?

Answer 14

The number of oscillations per second measured in hertz.

Question 15

What is the amplitude?

Answer 15

The maximum displacement of a particle from rest on that wave.

Question 16

Look at all the things against time/displacement in the paper version of the Cornell notes.

Answer 16

Do it in another 5 minutes if you do not see this card again. https://docs.google.com/document/d/1jTmQesIkik21kG9aYmp4GN2YzXJlvMpll4F1i6PQWTw/edit

Question 17

What are the conditions needed for SHM?

Answer 17

Acceleration is directly proportional to the displacement in the opposite direction. a is directly proportional to negative displacement (-x).