Waves; Topic 4.1 Oscillations

Question 1

What is the nature of an oscillation?

Answer 1

Oscillation motion is repetitive ie. periodic as it moves back and forth around an equilibrium position

Question 2

Define amplitude

Answer 2

The maximum displacement from the equilibrium position

Question 3

Define period

Answer 3

The time required to complete one cycle of a wave

Question 4

What is the meaning of isochronous waves?

Answer 4

If the oscillations have a constant period, they are said to be isochronous

Question 5

Define wavelength

Answer 5

the length of one complete oscillation measured from the same point on two consecutive waves

Question 6

Define frequency of a wave

Answer 6

the number of oscillations per second and it is measured in hertz (Hz)

Question 7

Simple harmonic motion (SHM) is defined as?

Answer 7

The motion of an object whose acceleration is directly proportional but opposite in direction to the object’s displacement from a central equilibrium position

Question 8

An object is said to perform simple harmonic oscillations when all of the following apply:

Answer 8

The oscillations are isochronous
Amplitude and period are constant and independent of each other
There is a central equilibrium point
The object’s displacement, velocity and acceleration change continuously
There is a restoring force always directed towards the equilibrium point
The magnitude of the restoring force is proportional to the displacement

Question 9

Define phase difference and how it is measured?

Answer 9

The phase difference between two waves is the horizontal distance a similar part of one wave leads or lags the other wave

Phase difference is measured in fractions of a wavelength, degrees or radians

Question 10

How to find phase difference?

Answer 10

This can be found from the relative position of the crests or troughs of two different waves of the same frequency

Question 11

What is in phase?

Answer 11

When the crests of each wave or the troughs of each wave are aligned, the waves are in phase
In phase is 0 degrees, a phase difference of 360 degrees is a time delay of one cycle which amounts to no phase shift at all

Question 12

What is anti-phase?

Answer 12

When the crest of one wave aligns with the trough of another, they are in antiphase
In anti-phase is 180 degrees or π radians

Question 13

What is the total energy of an object oscillating with SHM? Mention equation

Answer 13

The total energy of an object oscillating with SHM is the sum of its potential energy (gravitational or elastic) and kinetic energy
E = EP + EK

Where:
E = total energy in joules (J)
EP = potential energy in joules (J)
EK = kinetic energy in joules (J)

Question 14

Which forms of energy are at maximum or minimum at the point of maximum displacement from the equilibrium position?

Answer 14

The potential energy store of the object is at a maximum at the point of maximum displacement from the equilibrium position
The point of maximum displacement is amplitude x0
Kinetic energy is zero at amplitude
Potential energy is equal to the total energy of the system at this point

Question 15

What happens to energy as the oscillating system returns to equilibrium position from maximum displacement?

Answer 15

Energy is transferred from the object’s potential energy store to its kinetic energy store as the object moves from amplitude to the equilibrium position

The object has both potential and kinetic energy
The sum of the potential and kinetic energy is equal to the total energy of the system
The total energy of the system is conserved

Question 16

Which forms of energy are at maximum or minimum at the equilibrium position and why?

Answer 16

The kinetic energy store of the object is at a maximum at the equilibrium position
This is because velocity is at a maximum as the object passes through the equilibrium position
Kinetic energy is equal to the total energy of the system at this point

Question 17

What happens to energy as the oscillating system travels to the maximum displacement from equilibrium?

Answer 17

Energy is transferred from the object’s kinetic energy store to its potential energy store as the object moves from the equilibrium position to amplitude

The object has both potential and kinetic energy
The sum of the potential and kinetic energy is equal to the total energy of the system
The total energy of the system is conserved

Question 18

The defining conditions of simple harmonic oscillations are that the restoring force and the acceleration must always be:

Answer 18

Directed towards the equilibrium position, and hence, is always in the opposite direction to the displacement
Directly proportional to the displacement
a ∝ −x

Question 19

Relationship between force and displacement in SHM and graph

Answer 19

Force and displacement in SHM have a linear relationship where the gradient of the graph represents the constant
In this case, the spring constant k. Negative slope line passing through origin

Question 20

Define displacement

Answer 20

Displacement (x) of a wave is the distance of a point on the wave from its equilibrium position
It is a vector quantity; it can be positive or negative and it is measured in metres (m)

Question 21

One complete oscillation is:

Answer 21

1 wavelength
360°
2π radians

Question 22

The displacement-time graph for an object moving with SHM is a sinusoidal curve if

Answer 22

The object starts to oscillate from the equilibrium position.
The equilibrium position is x = 0 at t = 0

Question 23

The displacement-time graph is a cosine curve if

Answer 23

he object starts to oscillate from the position of maximum displacement.
Maximum displacement is x = x0 at t = 0

Question 24

What do the maxima and minima indicate in displacement time graphs?

Answer 24

The maxima and minima on the graph are the values of maximum displacement (x0) of the oscillating object on either side of the equilibrium position

Question 25

What does the gradient give in displacement time graphs of SHM

Answer 25

It gives the velocity by drawing a tangent to a point on the graph

Question 26

The velocity-time graph is a cosine curve if

Answer 26

The object starts to oscillate from the equilibrium position when x = 0 at t = 0
The displacement-time graph is a sine curve

Question 27

The velocity-time graph is a sine curve if:

Answer 27

The object starts to oscillate from the position of maximum displacement when x = x0 at t = 0
The displacement-time graph is a cosine curve

Question 28

What is the phase difference between displacement-time graph and velocity-time graph?

Answer 28

90 degrees or π/2 rad. (velocity time graphs have a contrasting trigonometric function graph to the displacement time graph)

Question 29

What do the maxima and minima indicate in velocity time graphs?

Answer 29

The maxima and minima on the graph are the values of maximum velocity (v0) of the oscillating object as it passes the equilibrium position

Question 30

How is the acceleration time graph obtained?

Answer 30

The acceleration-time graph is obtained by taking the gradients of tangents to all points on the velocity-time graph. Therefore acceleration is the gradient of a velocity-time graph for SHM

Question 31

The acceleration-time graph is a negative sine curve if:

Answer 31

The object starts to oscillate from the equilibrium position when x = 0 at t = 0 (when displacement-time graph is sine curve)

Question 32

The acceleration-time graph is a negative cosine curve if:

Answer 32

The object starts to oscillate from the position of maximum displacement when x = x0 at t = 0 (when displacement-time graph is cosine curve)

Question 33

What do the maxima and minima indicate in acceleration time graphs?

Answer 33

The maxima and minima on the graph are the values of maximum acceleration (a0) of the oscillating object at the positions of maximum displacement (x = x0)

Question 34

Phase difference between displacement-time and acceleration-time graphs of SHM

Answer 34

180 degrees or π

Question 35

State one similarity and two differences between the graphs

Answer 35

Note that all graphs must have the same period
The only two differences between the graphs are:
The shift in time - i.e. there is a phase difference of 90° between successive graphs
The amplitude of the wave form - i.e. the different amplitudes of the three graphs are the values of maximum displacement x0, maximum velocity v0 and maximum acceleration a0 of the oscillating object