Oscillations

Question 1

What happens when an object oscillates?

Answer 1

It moves back and forth about a fixed position

Question 2

What is a free oscillation?

Answer 2

Where an object oscillates freely after an initial disturbance

Question 3

Give an example of a free oscillator

Answer 3

A pendulum

Question 4

What is a forced vibration/oscillation?

Answer 4

When an object is forced to vibrate by an external source

Question 5

Give an example of a forced vibration/oscillation

Answer 5

Pushing a swing

Question 6

What is amplitude? (In the context of oscillations)

Answer 6

The maximum displacement from the equilibrium position

Question 7

What is frequency? (In the context of oscillations)

Answer 7

The number of oscillations per unit time

Question 8

What is angular frequency?

Answer 8

The number of radians per unit time

Question 9

What is the difference between angular velocity and angular frequency in oscillations?

Answer 9

Essentially no difference, except angular velocity is a vector, but angular frequency is a scalar

Question 10

What are the conditions for simple harmonic motion?

Answer 10

There must be a mass that oscillates, an equilibrium position and a restoring force that returns the mass to its central position

Question 11

Give examples of simple harmonic motion

Answer 11

A freely oscillating pendulum, molecules vibration in a sound wave

Question 12

What is the definition of simple harmonic motion?

Answer 12

A body executes simple harmonic motion if its force is proportional to its displacement from the equilibrium position, and is directed towards that point

Question 13

What does the graph of displacement against time for a freely oscillating pendulum look like?

Answer 13

A sin graph

Question 14

What does the graph of velocity against time for a freely oscillating pendulum look like?

Answer 14

A cos graph

Question 15

What does the graph of acceleration against time for a freely oscillating pendulum look like?

Answer 15

A -sin graph

Question 16

What is meant by a damped system?

Answer 16

One where the amplitude decreases over time as energy is removed from the system due to friction.
Frequency and time period remain constant, and there is an exponential pattern as more energy is removed while the system moves faster

Question 17

Give examples of a damped system

Answer 17

A pendulum, a trolley oscillating on springs, a mass on a spring in water

Question 18

What is meant by critical damping?

Answer 18

Critical damping is where the object returns to the equilibrium position in the shortest possible time without any oscillation

Question 19

Give examples of critically damped systems

Answer 19

An analogue meter, speedometer needle, modern elevators

Question 20

What sort of damping is used in car suspension?

Answer 20

Damping that is just less than critical

Question 21

What is meant by resonance?

Answer 21

A build up of large amplitude oscillation

Question 22

When does resonance occur?

Answer 22

When the frequency of the external driving force matches the natural frequency of the system, and the energy is transferred to the system in the most efficient way

Question 23

Outline an example of useful resonance

Answer 23

In microwave ovens. The external driving force is provided by the microwaves. The frequency of the microwaves matches the natural frequency of the water molecules which resonate and transfer energy to the food.

Question 24

Outline an example where resonance is a problem

Answer 24

Resonance in structures due to wind (like bridges, such as Tacoma narrows?), in buildings (avoiding having buildings with the same natural frequency of minor tremors)

Question 25

For a trolley and spring system, what do graphs for energy against displacement and energy against time look like?

Answer 25

Energy against displacement: elastic potential energy is a quadratic curve with a minimum at the origin, and kinetic energy is a negative quadratic with a maximum at x = 0
Energy against time: Kinetic energy is a cos graph and elastic potential energy is a sin curve (if assumed starting at 0 displacement and no friction)
Time period of this graph = 2 oscillations

Question 26

Explain the shapes of the graphs for the relationship of amplitude against frequency of the external force for systems with and without damping

Answer 26

• The graph for the system without damping has a much sharper and higher peak which is also slightly to the right of the graph for the system with damping
• The natural frequency is lower with damping as the resultant force is lower therefore acceleration is lower (so time period and natural frequency decrease)
• Amplitude of vibrations decreases as more energy is removed from the system
• The y intercept of this graph tells us the amplitude of the external oscillator