Module 5: Chapter 17 - Oscillations

Question 1

What is the equation for the time period of an oscillating pendulum?

Answer 1

T² = 4π² l/g

Question 2

What is the equation for the time period of an oscillating mass-spring system?

Answer 2

T² = 4π² m/k

Question 3

What is the equation for the time period of a conical pendulum?

Answer 3

T² = 4π² r/g(tanθ)

Question 4

Show how the equation for the time period of a conical pendulum is derived:

Answer 4

Question 5

What are the 2 criteria for an object to be undergoing simple harmonic motion?

Answer 5

• The acceleration of the object is towards a fixed point. The acceleration is the opposite direction to the displacement.
• The acceleration is proportional to the displacement of the object

Question 6

When is velocity greatest in simple harmonic motion?

Answer 6

When the displacement is 0

Question 7

When is the velocity zero in simple harmonic motion?

Answer 7

When the displacement is at a maximum

Question 8

When is the acceleration greatest in simple harmonic motion?

Answer 8

• When the velocity is 0
• When the displacement is at a maximum (in the opposite direction)

Question 9

When is the acceleration zero in simple harmonic motion?

Answer 9

• When the velocity is at a maximum
• When the displacement is 0

Question 10

What function describes displacement in simple harmonic motion?

Answer 10

a sinusoidal function

Question 11

What determines whether the displacement of a simple harmonic system is described by a sin graph or a cos graph?

Answer 11

The intial displacement

Question 12

When does a sin graph describe the displacement of a simple harmonic motion system?

Answer 12

When the displacement is initially 0

Question 13

When does a cosine graph describe the displacement of a simple harmonic motion system?

Answer 13

When the displacement is intially at a maximum

Question 14

What is the equation for the the displacement of a simple harmonic system?

assuming displacement starts at 0

Answer 14

x = A sin(ωt)

A = amplitude, ω = angular frequency/speed, t = time

Question 15

What is the equation for the velocity of a simple harmonic system?

assuming displacement starts at 0

Answer 15

• v = ωA cos(ωt)
• v = ±ω root(A² - x²)

x = displacement, A = amplitude, ω = angular frequency/speed, t = time

Question 16

What is the equation for the acceleration of a simple harmonic system?

assuming displacement starts at 0

Answer 16

• a = -ω²A sin(ωt)
• a = -ω²x

x = displacement, A = amplitude, ω = angular frequency/speed, t = time

Question 17

What is the equation for the maximum displacement of a simple harmonic system?

Answer 17

xₘₐₓ = A

Question 18

What is the equation for the maximum velocity of a simple harmonic system?

Answer 18

Vₘₐₓ = ωA

Question 19

What is the equation for the maximum acceleration of a simple harmonic system?

Answer 19

aₘₐₓ = -ω²A

Question 20

What is oscillating motion?

Answer 20

Repetitive motion of an object around its equilibrium position

Question 21

What is constant in simple harmonic motion?

Answer 21

• ω, angular frequency/speed
• T, time period

It is an isochronous oscillator!

Question 22

What is an isochronous oscillator?

Answer 22

An oscillator that has the same period regardless of amplitude (such as simple harmonic motion)

Question 23

What is damping?

Answer 23

An oscillation is damped when an external force that ocats on the oscillator has the effect of reducing the amplitude of its oscillations

Question 24

Describe the difference between light and heavy damping:

Answer 24

• Light Damping is when the amplitude of the oscillator gradually decreases with time, but the period of the oscillations is almost unchanged.
• Heavy Damping is when the amplitude decreases significantly, and the period of the oscillations will increase, there is hardly any oscillatory motion and the oscillator will move slowly back towards its equilibrium position

Question 25

Why does damping increase time period?

Answer 25

The damping force will act against the force of the oscillating motion, therefore the acceleration of the system will decrease causing the time to reach the equilibrium position to increase and therefore the time period

Question 26

What is free oscillation?

Answer 26

When a mechanical system is displaced from its equilibrium position and then allowed to oscillate without any external forces

Question 27

What is the natural frequency of an oscillator?

Answer 27

The frequency of free oscillation

Question 28

What is a forced oscillation?

Answer 28

An oscillation in which a periodic driver force is applied to an oscillator, the object will vibrate at the frequency of the driving force (driving frequency)

Question 29

What will happen if the driving frequency is equal to the natural frequency of an oscillator?

Answer 29

The system will resonate

Question 30

Explain which paper cone will oscillate with the largest frequency when pendulum D is oscillating at its natural frequency and why

Answer 30

The heavy pendulum D acts as a driver for the paper cone pendulums. Pendulum D oscillates at its natural frequency causing all the other pendulums to oscillate at the same frequency. As pendulum 2 is of the same length as pendulum D, it has the same natural frequency and will therefore resonate causing the amplitude to be greater than all the surrounding pendulums

Question 31

What is an example of light damping?

Answer 31

A pendulum oscillating in air

Question 32

What is an example of heavy damping?

Answer 32

A pendulum oscillating in water

Question 33

What is resonance?

Answer 33

The increase in amplitude of a forced oscillation when the driving frequency matches the natural frequency of the oscillating system

Question 34

What happens if a resonanting system is not damped?

Answer 34

The amplitude of the oscillation increases considerably, if not damped the amplitude will increase to the point at which the object fails

Question 35

What are examples of when resonance is utilised?

Answer 35

* Many clocks keep time using the resonance of a pendulum or a quartz crystal * Many musical instruments have bodies that resonate to produce louder notes * Some types of tuning circuits use resonance effects to select the correct frequency of radio wave signal * MRI (magnetic resonance imaging) enables diagnostic scans of the body without surgery or harmful x-rays

Question 36

What does damping a forced oscillation achieve?

Answer 36

* It **reduces the maximum amplitude** at resonance (and all other frequencies) * **Decreases the frequency** of when the maximum amplitude occurs * On a graph of "amplitude of forced oscillation" against driving frequency, there is a broader and flatter curve

Question 37

What type of oscillator is simple harmonic motion and why?

Answer 37

An **isochronous** oscillator, the time period is the same regardless of amplitude