Oscillations

Question 1

Define frequency:

Answer 1

The number of oscillations per second (Hz)

Question 2

Define the time period

Answer 2

The time taken for one complete oscillation (s)

Question 3

Define amplitude:

Answer 3

The maximum displacement from an equilibrium position

Question 4

Define Displacement

Answer 4

The distance from an equilibrium position.

Question 5

Natural frequency

Answer 5

The frequency at which an object will naturally vibrate when plucked.

Question 6

Resonance

Answer 6

When the frequency of the forced oscillator equals the natural frequency of the object, the object’s amplitude will increase to breaking point, as the energy transfer between the oscillator and the object is a maximum.

Question 7

Phase difference

Answer 7

Difference in radians or degrees between points on the same wave or points on two waves.

Question 8

Angular frequency

Answer 8

Is the product of 2pi x frequency
(Units of radians per second)

Question 9

Dampening

Answer 9

Energy due to motion is lost due to resistive forces such as air or shock absorbers of a car. This causes the amplitude of motion to decrease with time.

Question 10

When does an object execute simple harmonic motion?

Answer 10

-When the acceleration is directly proportional to the displacement.
-When the acceleration acts towards the equilibrium position

Question 11

Define x=Asin(wt)
And when is this equation used?

Answer 11

x = displacement (m)
A= amplitude (m)
w = 2pif = angular frequency/velocity (rads^-1)
t = time (s)
Used when the oscillator starts with x=0m, at equilibrium position at t=0s

Question 12

Define x=Acos(wt)
And when’s it used?

Answer 12

x =displacement (m)
A = amplitude (m)
w = angular frequency/ velocity (rads^-1)
t = time (s)
Used: when the oscillator starts of with x=A and at t=0s

Question 13

Maximum velocity equation:

Answer 13

vmax = Aw

vmax= maximum velocity
A= amplitude
w = angular frequency / velocity

Question 14

Equation for maximum acceleration:

Answer 14

amax = -w^2A
amax= maximum acceleration
w^2 = angular frequency squared
A = amplitude

Question 15

What’s an isochronous oscillator?

Answer 15

An isochronous oscillator has a time period that is independent of the amplitude for initially small amplitude.

Question 16

When do you achieve max velocity during SHM?

Answer 16

During equilibrium, when x=0

Question 17

When do you get max acceleration during SHM?

Answer 17

You get maximum amplitude when x=A

Question 18

How are acceleration and displacement related?

Answer 18

They are directly proportional to one another. However at max positive acceleration you have max negative displacement, they act in opposite directions to one another.

Question 19

At x=0 and x=A describe the kinetic energy store of the SHM system:

Answer 19

At x=0, the mass has a maximum velocity so the KE is a maximum
At x=A, the mass has zero velocity so the KE is zero

Question 20

How does the kinetic energy relate to the gravitational potential energy in a SHM system?

Answer 20

As KE increases, GPE decreases and vice versa.
This is for a closed system where there are no external energy transfers.

Question 21

How is an oscillator dampened?
What direction do the resistive forces act in?
When is the resistive force a maximum?

Answer 21

An oscillator is dampened if there is a resistive force acting on it
The resistive force is in the opposite direction to the velocity of motion
The resistive force is a maximum when the velocity is a maximum which occurs at x=0m

Question 22

Give examples of natural and artificial damping:

Answer 22

Natural: Air, Water
Artificial: Shock absorbers in buildings&cars, electromagnetic damping

Question 23

Define resonance:

Answer 23

When the frequency at which a force is applied to an object is equal to the natural frequency of the object, the energy transfer between driver and the object is a maximum. Therefore, the amplitude will increase to a maximum and we say the object resonates.

Question 24

How do you draw a dampened curve on a no damping curve?
The graph is amplitude against driving frequency.

Answer 24

• The maximum amplitude decreases
• The peak shifts to lower frequencies
• The range of amplitudes is always less
• The peak becomes broader