5.3 - Oscillations

Question 1

What is an oscillation?

Answer 1

A motion in which a body moves repeatedly backwards and forwards past a fixed point.

Aka periodic motion

Question 2

What causes an object to oscillate?

Answer 2

The object starts at an equilibrium position

A force is applied to the object, displacing it.

The object then begins to oscillate

Question 3

How does speed of an objet vary as it oscillates?

Answer 3

As it travels towards equilibrium, the speed increases

It slows down once it passes the equilibrium position, and eventually reaches maximum displacement (amplitude), where the object is stationary

It then moves back towards equilibrium, speeding up, then slows down again as it passes equilibrium.

This is repeated over and over again

Question 4

What is displacement?

Answer 4

The distance from the equilibrium position

• symbol = x
• unit = metres

Question 5

What is amplitude?

Answer 5

The maximum displacement from the equilibrium position

• symbol = A
• units = metres

Question 6

What is the period of an oscillation?

Answer 6

The time taken to complete one full oscillation

• symbol = T
• units = seconds

Question 7

What is the frequency of an oscillation?

Answer 7

The number of complete oscillations per unit time

• symbol = f
• units = Hz

Question 8

What is phase difference (for oscillating motion)?

Answer 8

The difference in displacement between two oscillating objects

Or difference in displacement of an oscillating object at different times

• symbol φ
• measured in radians

Question 9

What’s angular frequency?

Answer 9

A term used to describe the motion of an object

Closely related to angular velocity (circular motion)

Question 10

What are the equations for angular frequency?

Answer 10

ω = (2π)/T
• ω = angular frequency, rad s^-1
• T = period of the oscillator, s

ω = 2πf
• ω = angular frequency, rad s^-1
• f = frequency of oscillator, Hz

Question 11

What is simple harmonic motion?

Answer 11

The acceleration of the oscillator is directly proportional to the displacement

The acceleration of the object acts in the opposite direction of the displacement, toward the position of equilibrium

Question 12

What is the equation for SHM?

Answer 12

a = -ω²x

Where:
• a = acceleration
• ω = angular frequency
• x = displacement

Question 13

what is an isochronous oscillator?

Answer 13

an oscillator undergoing SHM

the time period, T, of an isochronous oscillator is independent of the amplitude.

This is because as the amplitude increases, so does the average speed of the swing (due to increasing acceleration) so the period does not change

Question 14

How can you determine the frequency/time period of an oscillator undergoing SHM?

Answer 14

1) set up a pendulum hanging freely from a clamp stand.
2) place a fiducial marker at the equilibrium position
3) displace the pendulum by no more than 15 degrees
4) start the stop clock when the oscillator passes the equilibrium position. time how long it takes for 10 full oscillations to occur.
5) divide this tome by 10 to get the time period of the oscillator.
6) find the reciprocal of the time period to get the frequency

Question 15

How can you calculate displacement of a pendulum form a displacement-time graph?

Answer 15

x = Acosωt
or
x = Asinωt

Where:
• x = displacement
• A = amplitude
• ω = angular frequency
• t = time

NOTES:
• the equation you use depends on whether t=0 is at the amplitude (cosine) or equilibrium (sin)
• the calculator must be in radians for these calculations

Question 16

What is the equation for velocity of an oscillator undergoing SHM?

Answer 16

v = ±ω√(A²-x²)

Where:
• v = velocity
• ω = angular frequency
• A = amplitude
• x = displacement

Question 17

What is the equation for the maximum velocity of an oscillator?

Answer 17

v = ωA

Where:
• v = velocity
• ω = angular frequency
• A = amplitude