Chapter 17 - Oscillations

Question 1

Define these SHM terms:
Displacement
Amplitude
Period
Frequency

Answer 1

Displacement, x - the distance from the equilibrium position.
Amplitude, A - the maximum displacement.
Period, T - the time taken to complete one full oscillation,
Frequency, f - the number of complete oscillations per unit time.

Question 2

Phase Difference of an oscillation

Answer 2

The fraction of an oscillation between the position of two oscillating objects. Symbol Φ
Δt/T x 2π

Question 3

Angular Frequency in SHM

Answer 3

The rate of change of angular position. Symbol ω
2πf

Question 4

What is Simple Harmonic Motion?

Answer 4

Acceleration is directly proportional to the displacement
Acceleration always acts towards the equilibrium position.
Isochronous oscillation, the period is independent to the amplitude.

Question 5

Acceleration in SHM

Answer 5

a = -ω²x

Question 6

Investigating SHM

Answer 6

The frequency is equal to the inverse of the time period. So if we time the period we can get the frequency. It’s best to record the time for 10 oscillations then divide that by 10 to reduce inaccuracy.

Question 7

Displacement Equation SHM

Answer 7

x = Asin(ωt) or x = Acos(ωt)
Sin or Cos depends on starting position.

Question 8

SHM the link between Displacement, Velocity and Acceleration

Answer 8

·Maximum Acceleration and 0 velocity at maximum displacement.
·Graph of displacement is a reflection in the x axis of graph of acceleration.

Question 9

Velocity Equation SHM

Answer 9

v = ±ω√(A² - x²)

Question 10

Energy Changes in during SHM

Answer 10

Bell curves of Potential Energy and Kinetic Energy, energy against displacement.
At any displacement, Kinetic Energy + Potential Energy = Constant.

Question 11

Damping

Answer 11

Damping is the process by which the amplitude of the oscillation decreases over time. This is due to resistive forces.

Question 12

Types of Damping

Answer 12

Light Damping - Amplitude decreases slowly and exponentially, ie air resistance.
Heavy Damping - Amplitude decreases dramatically, ie oscillating in water.
Critical Damping - The object stops before one oscillation is completed.

Question 13

Natural Frequency

Answer 13

When an object oscillates without any external forces being applied, it oscillates at its natural frequency. This is known as free oscillation.

Question 14

Forced Oscillation

Answer 14

A periodic driving force is applied to the object, causing it to oscillate at a certain frequency.

Question 15

Resonance

Answer 15

Resonance is when the driving frequency of an external force is equal to the natural frequency, causing the amplitude of oscillation to rapidly increase until the system fails.

Question 16

Damping Effect on Resonance

Answer 16

As damping increases, the amplitude will decrease at all frequencies and the maximum amplitude occurs at a lower frequency.
Graph is transformed down and left.

Question 17

Investigating Resonance

Answer 17

· Mass Suspended between 2 springs attached to an oscillating generator.
· A ruler placed parallel to the springs next to the mass to record the amplitude.
· Slow increase the driving frequency, taking amplitude readings at certain internals.
· Keep increasing the driving frequency until the amplitude begins to decrease again.
· System is damped by air resistance so system wont break.
· Plot a graph to show the variation of amplitude and driving frequency. The peak formed is the natural frequency.