Definitions 4: Oscillation, Circular and Wave Motion, Superposition

Question 1

Angular Displacement (θ)

Answer 1

The angle swept out by the radius.
θ is in radians.
θ has a magnitude and direction (clockwise/anticlockwise).

Question 2

Radian

Answer 2

The angle subtended at centre of circle by an arc equal in length to the radius.

Question 3

Angular Velocity (ω)

Answer 3

The rate of change of angular displacement swept out by the radius.
ω is in rad s-1.
Points lying on the same radius will have equal angular velocity.

Question 4

Linear Velocity (v)

Answer 4

Linear velocity is the velocity of a body at a particular point along its circular motion along the tangent drawn to the circular path.

Also known as tangential velocity as the direction of the linear velocity of a body at any point along its circular motion is along a tangent drawn to its circular path.

Question 5

Uniform Circular Motion

Answer 5

An object in uniform circular motion is moving in a circle at constant speed.

Question 6

Centripetal Force

Answer 6

Centripetal force is the force directed towards the centre of a circle that is required for an object to travel in a circular path.

It can be the result of a single force of a combination of forces pointing towards the centre of the circle

It must not be drawn in the free body diagram since it is a resultant force.

Centripetal force does no work.

Question 7

Oscillation

Answer 7

The repetitive back and forth motion of an object along the same path.

Question 8

Free oscillation

Answer 8

When a system is displaced from equilibrium state and is then allowed to move or respond without restraint. There is no external force applied or resisting its motion (only restoring force present). As such there is no gain or loss of total energy of the oscillating system.

Question 9

Natural frequency

Answer 9

The frequency at which a system will oscillate at when there is no driving force/external force acting on it.

Question 10

Simple Harmonic Motion (SHM)

Answer 10

Simple Harmonic Motion is a type of oscillatory motion whose acceleration is always directly proportional to its displacement from the equilibrium position and is always directed opposite to its displacement/towards the equilibrium position.

Question 11

Equilibrium position

Answer 11

The position of the mass where no net force acts on the oscillating mass.

Question 12

Displacement (x)

Answer 12

The distance in a specified direction from its equilibrium position.

Question 13

Amplitude (x^o)

Answer 13

Maximum displacement of the oscillating mass from the equilibrium position.

Question 14

Period (T)

Answer 14

Time taken for one complete oscillation of the oscillating mass.

Question 15

Frequency (f)

Answer 15

Number of complete oscillations per unit time made by oscillating mass.

Question 16

Phase (ɸ)

Answer 16

The angular measure of the fraction of a cycle that has been completed by the oscillating mass. One complete cycle corresponds to a phase ϕ=360° or 2π radians.

Question 17

Phase Difference (Δɸ)

Answer 17

The measure of how much an oscillation is out of step with itself at 2 different instances in time, or how much 2 oscillations are out of step with each other at the same instant in time.
In phase: Phase difference is zero
Out of phase: Phase difference is not zero
Antiphase: Phase difference is 180° or π radians

Question 18

Angular frequency (ω)

Answer 18

The product of 2π and the frequency.

Question 19

Damped oscillation

Answer 19

An oscillation where there are resistive forces present to cause the oscillator to lose energy until it comes to a stop.

Question 20

Degree of damping

Answer 20

Amount of resistance to motion the oscillator is subjected to and can range from light to heavy damping

Light damping: The system is still oscillating but the amplitude decreases over time. The period of oscillation is longer than in the case of no damping
Critical damping: Degree of damping where damping is strong enough such that no oscillation takes place, and the oscillator takes the shortest amount of time to reach equilibrium. (point of transition between light and heavy damping)
Heavy damping: The system does not oscillate, ie. does not go past equilibrium

Question 21

Forced oscillation

Answer 21

An oscillation where continuous energy input is provided to the oscillating system by an external periodic force which is known as a driving oscillator. It is made to vibrate at the frequency of the external driver.

Question 22

Driving frequency

Answer 22

The frequency of the driving force, which may be different from the natural frequency of the oscillator.

Question 23

Resonance

Answer 23

The phenomenon in which there is maximum transfer of energy from the driver to the oscillator. It occurs when the driving frequency matches the natural frequency of the undamped oscillator. The oscillations achieve maximum amplitude.

Question 24

Principle of Superposition

Answer 24

When two or more waves overlap at a point, the resultant displacement is the sum of the individual displacements of each wave at that point → Amplitude adds up, NOT intensity

Question 25

Constructive/destructive interference

Answer 25

Constructive Interference: When waves meet at a point such that the resultant displacement is larger than the largest individual displacement → waves meet in phase

Destructive interference: When waves meet at a point such that the resultant displacement is lesser than the largest individual displacement → waves meet in antiphase

Question 26

Stationary wave

Answer 26

Formed when 2 progressive waves of the same type, amplitude, frequency and speed travelling in opposite directions overlap.

Question 27

Nodes/Antinodes

Answer 27

Node: Points of maximum fluctuation in amplitude

Antinode: Points of no displacement

Question 28

Diffraction

Answer 28

Phenomenon where a wave spreads out after passing through a slit or around the edge of an obstacle.

Question 29

Coherence

Answer 29

Sources are coherent if they produce waves with constant phase difference → only possible for same type, wavelength and frequency

Question 30

Path difference

Answer 30

Path difference to a point is the difference in distance from one source to that point and the distance from another source to that point.

Question 31

Resolution

Answer 31

Resolution of two objects is the ability to see as two distinct objects that are distinct.

Question 32

Rayleigh Criterion

Answer 32

When two objects are just resolved, they can be distinguished. This happens when the first minimum of the diffraction pattern of one source coincides with the central maximum of the diffraction pattern of the other source.