13 - Oscillations

Question 1

What are the two conditions required for an object to oscillate with SHM?

Answer 1

1. The restoring force is directly proportional to the displacement.
2. The restoring force always acts towards the equilibrium position.

Question 2

What is angular frequency?

Answer 2

Angular frequency is a measure of the rate of rotation of an object.

Question 3

Give two equations for angular frequency.

Answer 3

Ω = 2π/T
Ω = 2πf

Question 4

What are the two types of oscillations that an object can experience?

Answer 4

Free oscillations
Forced oscillations

Question 5

What is the frequency of a freely oscillating object equal to?

Answer 5

Freely oscillating object will vibrate at their natural frequency.

Question 6

What is resonance?

Answer 6

Resonance is where the amplitude of oscillations of an object drastically increase due to gaining an increased amount of energy from the driving force.
This occurs when the driving frequency equals the natural frequency of the object.

Question 7

What can be said about an object undergoing resonance?

Answer 7

The object will be oscillating at its maximum amplitude and the rate of energy transfer is at a maximum.

Question 8

What is damping?

Answer 8

Damping occurs when energy is lost from an oscillating system due to an external force acting on it.

Damping is the process by which energy is dissipated in an oscillating system, leading to a reduction in the amplitude of oscillations over time.

Question 9

What are the three types of damping?

Answer 9

1. Light Damping
2. Critical Damping
3. Heavy Damping

Question 10

What is critical damping?

Answer 10

Critical damping is when the damping causes the object to return to the equilibrium position in the quickest time possible without oscillating.

Question 11

State the equation for the total energy stored in a simple harmonic oscillator.

Answer 11

Energy stored = ½ kA^2
Where k is the spring constant, and A is the amplitude.

Question 12

If the following graph shows displacement against time, what would the velocity-time graph look like?

Answer 12

Question 13

If the following graph shows displacement against time, what would the acceleration-time graph look like?

Answer 13

Question 14

What is the difference between free and forced oscillations?

Answer 14

When an object oscillates without any external forces being applied, it oscillates at its natural frequency.
This is known as free oscillation. Forced oscillation occurs when a periodic driving force is applied to an object, which causes it to oscillate at a particular frequency.

Question 15

3 different types of how damping occurs

Answer 15

Viscous damping
Coulomb damping
Structural damping

Question 16

What is viscous damping

Answer 16

Resistance from a fluid (like air or oil) that opposes the motion of the oscillating object. The damping force is proportional to the velocity of the object

Question 17

What is coulomb damping

Answer 17

Friction between sliding surfaces, which remains nearly constant and depends on the characteristics of the surfaces

Question 18

What is structural damping

Answer 18

Internal friction within the material itself, often due to microscopic movements within the material’s structure

Question 19

Describe energy in simple harmonic motion

Answer 19

Energy is conserved
The energy changes from kinetic energy to potential energy

Question 20

What are free vibrations

Answer 20

They are not affected by any external varying forces
E.g a child on a swing will oscillate at a frequency that depends on the strength of the gravity and the length of the swing
The swing is said to oscillate with natural frequency

Question 21

What are forced vibrations

Answer 21

When a system is made to oscillate by an external periodic force
E.g a loudspeaker is made to oscillate by the oscillating electrical signal from an amplifier

Question 22

Light damping vs heavy damping

Answer 22

Light damping - the oscillations take a long time to fade away
Heavy damping - causes the object to oscillate hardly at all

Question 23

Explain resonance

Answer 23

All objects have their own natural frequency
If the driving frequency is the same as the natural frequency the amplitude of vibration increases
This is called resonance

Question 24

Equation for spring constant of springs in series vs parallel

Answer 24

Series:
1/k1 + 1/k2 = 1/kt
Parallel
K1 + k2 = kt

Question 25

Explain how the plastic deformation of ductile materials reduce the amplitude of oscillation.

Answer 25

The plastic deformation of a ductile material can be used to ​reduce the amplitude of oscillations​, this happens because ​energy is used to deform the material​, decreasing the kinetic energy of the system and so the amplitude of oscillations ...

Question 26

Use a climbing rope to explain how plastic deformation reduces the amplitude of oscillation

Answer 26

A climbing rope is different from a rescue rope or a bungee cord: A climbing rope is designed to extend when loaded suddenly The rope stretches to reduce the amplitude of the oscillation when a climber falls onto it It provides critical damping by immediately stopping the climber from bouncing

Question 27

Explain the resonance curve

Answer 27

When f < f0, the amplitude of oscillations increases At the peak where f = f0, the amplitude is at its maximum. This is resonance When f > f0, the amplitude of oscillations starts to decrease The maximum amplitude of the oscillations occurs when the driving frequency is equal to the natural frequency of the oscillator

Question 28

As the degree of damping is increased, how is the resonance graph altered

Answer 28

The amplitude of resonance vibrations decrease, meaning the peak of the curve lowers The resonance peak broadens The resonance peak moves slightly to the left of the natural frequency when heavily damped

Question 29

Describe a free oscillation

Answer 29

An oscillation where there are only internal forces (and no external forces) acting and there is no energy input A free vibration always oscillates at its resonant frequency

Question 30

What is the driving force

Answer 30

In order to sustain oscillations in a simple harmonic system, a periodic force must be applied to replace the energy lost in damping This periodic force does work against the resistive force responsible for decreasing the oscillations It is sometimes known as an external driving force

Question 31

What are forced oscillations

Answer 31

Oscillations acted on by a periodic external force where energy is given in order to sustain oscillations Forced oscillations are made to oscillate at the same frequency as the oscillator creating the external, periodic driving force For example, when a child is on a swing, they will be pushed at one end after each cycle in order to keep swinging and prevent air resistance from damping the oscillations These extra pushes are the forced oscillations, without them, the child will eventually come to a stop

Question 32

Describe the energy changes for an oscillation

Answer 32

At the amplitude of its oscillations the system will have the maximum amount of potential energy, as it moves towards the equilibrium position, this potential energy is converted to kinetic energy so that at the centre of its oscillations the kinetic energy is at a maximum, then as the system moves away from the equilibrium again, the kinetic energy is transferred to potential energy until it is at a maximum again and this process repeats for one full oscillation.

Question 33

What is the combined effect of damping and plastic deformation on an oscillation

Answer 33

Both damping and plastic deformation work to dissipate energy from the oscillating system, leading to a gradual reduction in amplitude. Damping converts kinetic energy into heat, while plastic deformation absorbs energy through permanent changes in the material's structure

Question 34

Why does the fiducial marker have to be at the mid point

Answer 34

As travelling fastest this point so effect if reaction time is reduced