Chapter 17 - Oscillations

Question 1

Features of oscillating objects

Answer 1

1. Have an equilibrium position
2. Are displaced by a force
3. Speed up when moving towards the equilibrium position and slow down when moving away from it
4. Will all eventually return to their equilibrium position

Question 2

Phase difference (φ)

Answer 2

The difference in displacement of two oscillating bodies or the displacement of one oscillating body at different times
In terms of 2π

Question 3

Angular frequency (ω)

Answer 3

2πf or 2π/t

Units rad s^-1, works largely the same way as angular velocity

Question 4

Simple harmonic motion

Answer 4

A form of oscillation where the acceleration of the object is directly proportional to the displacement and is always in the opposite direction

Question 5

SHM acceleration

Answer 5

a = -(ω^2 x)

Question 6

SHM time period and amplitude

Answer 6

They are independent as increasing the amplitude increases the average speed of the swing so the period does not change

Question 7

SHM displacement-time graph

Answer 7

If the displacement is a maximum at t=0, it will be a cosine graph
If the displacement is 0 at t = 0, it will be a sine graph

Question 8

SHM acceleration-time graph

Answer 8

An inverted displacement-time graph

Question 9

SHM displacement formulae

Answer 9

x=Acos(ωt)
x=Asin(ωt)

Use cos when the displacement at t = 0 is not 0

Question 10

SHM velocity formula

Answer 10

v = +/- ω x √(A^2 - x^2)

Question 11

SHM maximum velocity formula

Answer 11

vmax = ωA

Question 12

Energy-displacement graph for an oscillating object in SHM

Answer 12

Two parabolic curves for Ek and Ep
At x = 0 the Ek is a maximum and Ep 0
At x = +/- A, the Ek is 0 and Ep a maximum
The total energy is constant

Question 13

Total energy of a spring in SHM

Answer 13

1
– k A^2
2

Question 14

Kinetic Energy of a Spring in SHM

Answer 14

1
– k (A^2 - x^2)
2

Question 15

Damping

Answer 15

External forces acting on an oscillator opposing its velocity which reduce the amplitude of the oscillation.

Question 16

Damping

Answer 16

External forces acting on an oscillator opposing its velocity which reduce the amplitude of the oscillation.

Question 17

Light damping

Answer 17

Damping forces are small, amplitude reduces gradually, period of the oscillation almost unchanged
e.g. pendulum in air

Question 18

Heavy damping

Answer 18

Damping forces are large, amplitude decreases significantly, period of oscillation increases slightly
e.g. pendulum in water

Question 19

Very heavy damping

Answer 19

Damping forces are very large, no oscillating motion, oscillator just moves to equilibrium position
e.g. pendulum in treacle

Question 20

Displacement-time graph light damping

Answer 20

Follows the same cosine shape with a gradually reducing amplitude

Question 21

Displacement-time graph heavy damping

Answer 21

Displacement reduces to a slight negative before returning to the equilibrium position and remaining there

Question 22

Displacement-time graph very heavy damping

Answer 22

Gradually decreasing amplitude before it continues along the equilibrium position (never becomes negative) - almost like a reciprocal curve

Question 23

Free oscillation

Answer 23

Object displaced from equilibrium position and allowed to oscillate freely without external forces

Question 24

Natural frequency of an oscillator

Answer 24

The frequency of the free oscillation

Question 25

Forced oscillation

Answer 25

A periodic driver force is applied to an oscillator. The object will vibrate at the frequency of the driving force (driving frequency)

Question 26

Driving

Answer 26

If a force has the same driving frequency as the natural frequency of the oscillator, it will cause the amplitude of the oscillation to greatly increase.

Question 27

Barton’s pendulum

Answer 27

The oscillating bob will cause the amplitude of the cone pendulum with the same natural frequency as the bob’s driving frequency to increase

Question 28

Resonance

Answer 28

The amplitude of an oscillation increases considerably where the driving frequency of a forced oscillation is the same as the natural frequency of an oscillating object

Question 29

Resonance with no damping

Answer 29

The amplitude will keep increasing until the object fails

Question 30

Resonance uses:

Answer 30

Clocks using the resonance of a pendulum
Musical instruments resonate to make music louder
Tuning circuits to select the correct frequency

Question 30

Stronger damping effect on resonance

Answer 30

• Decreases the maximum amplitude of resonance
• Decreases the frequency at which resonance occurs
• The peak of the amplitude against frequency to widen

Question 31

How does MRI work?

Answer 31

• The scanner has a strong magnetic field which causes hydrogen nuclei inside the body to precess
• Radio waves emitted from coils inside the scanner cause the nuclei to resonate and absorb energy
• When the radio waves are switched off, the hydrogen nuclei re-emit the energy gained as photons
• These are detected by receiving coils and the signals are processed by computers to create a 3D image