Chapter 5 - Oscillations

Question 1

Define natural frequency?

Answer 1

The unforced frequency of oscillation of a freely oscillating object.

Question 2

What are forced oscillations?

Answer 2

When each oscillation has to be forced by something else.

Question 3

What are free oscillations?

Answer 3

Free oscillations occur when an object oscillates at its natural frequency, so it continues to oscillate after the initial disturbance.

Question 4

Define period?

Answer 4

The time taken for one complete oscillation of an object.

Question 5

Define frequency?

Answer 5

The number of oscillations of a particle per unit time.

Question 6

Define amplitude?

Answer 6

The maximum displacement of a particle from its equilibrium position.

Question 7

Define phase difference?

Answer 7

The fraction of an oscillation between the vibrations of two oscillating particles, expressed in radians.

Question 8

Define phase?

Answer 8

Phase describes the point that an oscillating mass has reached in a complete cycle.

Question 9

Define simple harmonic motion?

Answer 9

Motion of an oscillator where it’s acceleration is directly proportional to its displacement from its equilibrium position and is directed towards that position.

Question 10

Three requirements for SHM?

Answer 10

1) a mass that oscillates
2) a position where the mass is in equilibrium
3) a restoring force that acts to return the mass to its equilibrium position

Question 11

What is the restoring force directly proportional to in SHM?

Answer 11

Displacement

Question 12

Define angular frequency?

Answer 12

The rate of change of angle expressed in radians per second (ω).

Question 13

ω = ?

Answer 13

2πf = 2π/T

Question 14

When x=0 @ t=0?

Answer 14

x=Asin(2πft)

Question 15

When x=A @ t=0?

Answer 15

x=Acos(2πft)

Question 16

Because a is porportional to -x, what can we deduce?

Answer 16

a= -x(2πf)^2

Minus since always accelerating towards equilibrium position.

Question 17

Vmax = ?

Answer 17

Vmax = (2πf)A

Question 18

When do the maximum PE and KE points happen?

Answer 18

PE is maximum at the amplitude.

KE is maximum at x=0.

Question 19

Energy against time graph for SHM?

Answer 19

PE starts at max because system is starting at A. This means KE is at zero.
When the system is released KE increases and PE decreases, causing a two sine waves in antiphase.

ENERGY REMAINS CONSTANT.

Question 20

Energy against amplitude graph?

Answer 20

Symmetrical about y axis.

As you approach A, KE falls and PE rises. At x=0, PE is minimum, KE is maximum.

Question 21

Define damped, and 2 points about it?

Answer 21

Describes an oscillatory motion where the amplitude decreases with time due to energy losses.

1) causes displacement to decreases exponentially
2) used in car suspension - springs have shock absorber so the car doesn’t continuously bounce.

Question 22

Define resonance?

Answer 22

The forced motion of an oscillator characterised by max amplitude when the forcing frequency matches the oscillator’s natural frequency.

Question 23

For resonance to occur, the system has to absorb maximum energy. When will this occur?

Answer 23

When the source frequency = natural frequency of the system

Question 24

Three points for a system in resonance?

Answer 24

1) natural frequency is equal to driver frequency
2) amplitude is maximum
3) it absorbs greatest possible energy from the driver

Question 25

Describe a amplitude against driver frequency graph?

Answer 25

The amplitude of the system reaches a maximum at the peak of the line when natural frequency = driver frequency.

Question 26

Explain what happens to the graph of amplitude against driver frequency, with damping?

Answer 26

With damping, the peak (A) is lower, and moves to a slightly lower resonance frequency(left). Also, the peak becomes broader.

Question 27

Where is resonance used?

Answer 27

In instruments, MRI and microwaves. In microwaves, it is used to vibrate the water molecules at their natural frequency,

Question 28

Define oscillation?

Answer 28

A repetitive back and forth motion about the equilibrium position.