Oscillations

Question 1

Formula for angular frequency

Answer 1

w=2πf

Question 2

Relationship between acceleration and displacement.

Recall the graph for the relationship, stating three characteristics

Answer 2

a=-(w^2)x

Refer to image 1,

• Max acceleration at amplitude,
• Negative gradient show a and x in opp. direction
• Straight line passing through origin show a proportional to x

Question 3

Recall velocity-displacement graph, stating two characteristics

Answer 3

Refer to image 2,

Max velocity at equilibrium, zero velocity at amplitudes

Question 4

Relationship between displacement and time when

a) Equilibrium at t=0
b) Amplitude at t=0

Answer 4

a) x=x0 sin(wt)

b) x=x0 cos(wt)

Question 5

Recall x-t, v-t and a-t graph for when starting at equilibrium position

Answer 5

Refer to image 3

Question 6

Phase difference of particles…

a) in phase
b) out of phase
c) in antiphase

Answer 6

a) △ɸ = 0
b) 0 < △ɸ < 2π
c) △ɸ = π

Question 7

Phase difference formula + condition when using it

Answer 7

△ɸ = △t/T x 2π , oscillations must have same period/frequency

Question 8

Where does a) Max KE and b)Zero KE occur

Answer 8

a) Equilibrium

b) Amplitude

Question 9

Formula for KE and max KE

Answer 9

Sub v=… into 1/2mv^2.

Sub max v =…. into 1/2mv^2

Question 10

How to find total energy and potential energy?

Answer 10

TE = Max KE

TE - KE = PE

Question 11

What is damped oscillation?

Answer 11

Oscillation where amplitude decreases due to dissipative forces

Question 12

What are the 4 different degrees of damping?

Recall the respective graphs.

Answer 12

Refer to image 4

Question 13

Define resonance

Answer 13

When driving frequency = natural frequency, giving max. amplitude

Question 14

How does damping affect forced oscillations?

Answer 14

• Decreased amplitude
• Broader resonant peak
• Resonant peak occurs at lower frequencies