5.3 Oscillations

Question 1

Define displacement.

Answer 1

The distance from the equilibrium position.

Question 2

Define amplitude.

Answer 2

The maximum displacement.

Question 3

Define period.

Answer 3

The time taken to complete one complete oscillation.

Question 4

Define frequency.

Answer 4

The number of oscillations per unit time.

Question 5

Define angular frequency.

Answer 5

The rate of change of angular position.

Question 6

What are the units of angular frequency?

Answer 6

rad s⁻¹

Question 7

Define phase difference.

Answer 7

The fraction of an oscillation between the position of two oscillating objects.

Question 8

The equation for simple harmonic motion is 𝑎 = − 𝜔²x. What are the two conditions for simple harmonic motion to occur?

Answer 8

• The acceleration is proportional to the displacement
• The acceleration is always directed towards the equilibrium position

Question 9

There are two equations which can be used to determine the displacement of a simple harmonic oscillator: 𝑥 = 𝐴 sin(𝜔t) and 𝑥 = 𝐴 cos (𝜔t).
When do you use the sine version, and when do you use the cosine version?

Answer 9

• Use the sine version if the oscillator begins at the equilibrium position
• Use the cosine version if the oscillator begins at the amplitude position.

Question 10

Oscillations in simple harmonic motion are isochronous. What does this mean?

Answer 10

The period of the oscillation is independent of the amplitude.

Question 11

During simple harmonic motion, energy is exchanged between kinetic and potential forms. When does the maximum kinetic energy occur?

Answer 11

At the equilibrium point, when the velocity is at a maximum.

Question 12

During simple harmonic motion, energy is exchanged between kinetic and potential forms. When does the maximum potential energy occur?

Answer 12

At the amplitude positions, when displacement is at a maximum.

Question 13

What does the graph of displacement against time look like for simple harmonic motion?

Answer 13

A cosine or sine wave with the initial value of displacement at time = 0 being the amplitude, and a maximum value of the amplitude.

Question 14

What is the maximum value of a graph of velocity against time for simple harmonic motion, and how does its position relate to the graph of displacement against time?

Answer 14

Its maximum value is 𝜔A, it is a quarter of a cycle in front of the displacement.

Question 15

What is the maximum value of a graph of acceleration against time for simple harmonic motion, and how does its position relate to the graph of displacement against time?

Answer 15

It has a maximum value of 𝜔²A and is in antiphase with the displacement.

Question 16

What is the difference between free oscillations and forced oscillations?

Answer 16

A free oscillation is where there are only internal forces acting and there is no energy input, whereas a forced oscillation has a periodic external force where energy is given in order to sustain oscillations.

Question 17

What is damping?

Answer 17

The reduction in energy and amplitude of oscillations due to resistive forces on the oscillating system.

Question 18

What effect does damping have on amplitude and time period?

Answer 18

• The amplitude decreases
• The time period remains the same (remember: in simple harmonic motion the time period is independent of the amplitude)

Question 19

What is resonance?

Answer 19

An increase in amplitude that occurs when the frequency of the driving oscillator is similar to the natural frequency of the oscillator.

Question 20

What is natural frequency?

Answer 20

The frequency at which the system oscillates when no external forces act.