TOPIC 10: OSCILLATIONS

Question 1

[Definition] Oscillation

Answer 1

An oscillation is a to-and-fro motion between two limits

Question 2

[Definition] Free Oscillations

Answer 2

Free oscillations are oscillations with constant amplitude AND without energy loss or gain as there is no driving or resistive forces acting on it

Question 3

[Definition] Natural Frequency

Answer 3

Natural frequency is the frequency at which a body will vibrate when there is no driving or resistive forces acting on it

Question 4

[Definition] Equilibrium Position

Quantities of Oscillation

Answer 4

Position where no net force acts on the oscillating mass

Question 5

[Definition] Displacement, x

Quantities of Oscillation

Answer 5

Distance in a specified direction from equilibrium position of oscillating mass

Question 6

[Definition] Amplitude, x₀

Quantities of Oscillation

Answer 6

Maximum distance from equilibrium position

Question 7

[Definition] Period, T

Quantities of Oscillation

Answer 7

Time taken for one complete oscillation of the oscillating mass

Question 8

[Definition] Frequency, f

Quantities of Oscillation

Answer 8

Number of complete oscillations per unit time

Question 9

[Definition] Phase, ϕ

Quantities of Oscillation

Answer 9

An angular measure of the fraction of a cycle completed by the oscillating mass

Question 10

[Definition] Phase Difference, Δϕ

Quantities of Oscillation

Answer 10

Measure of how much an oscillation is out of step with another oscillation

Question 11

[Definition] Angular frequency

Quantities of Oscillation

Answer 11

Defined as the product of 2π and frequency

ω = 2πf (units: radian s⁻¹)

Question 12

[Definition] Simple Harmonic Motion

Answer 12

SHM is a type of oscillatory motion where the acceleration is directly proportional to the displacement from the equilibrium position and directed opposite to displacement

Question 13

[Formula] Main Formulas of Oscillation

Variation with x

Answer 13

a = - ω²x
v = ±√(x₀² - x²)

Question 14

[Formula] Main Formulas of Oscillation

Variation with t

Answer 14

If x = 0
x = x₀ sin(ωt)
v = ωx₀ cos(ωt)
a = - ω²x₀ sin(ωt)

If x = x₀
x = x₀ cos(ωt)
v = - ωx₀ sin(ωt)
a = - ω²x₀ cos(ωt)

Question 15

Finding equations for horizontal spring-mass systems

Answer 15

Combine with topic on Forces

F = ma = kx
a = - ω²x

to find ω, f, T etc

Question 16

Finding equations for vertical spring-mass systems

Answer 16

Combine with topic on Forces
F = ma
kx = ma
a = - ω²x
to find ω, f, T etc

Question 17

Finding equations for simple pendulum

Answer 17

Combine with topic on Forces
F = ma
mg sinθ = ma
a = - ω²x
to find ω, f, T etc

Question 18

Finding energy of oscillations

Answer 18

1. Always find kinetic energy first
2. Followed by total energy (when Ek max)
3. Potential energy

Same for both (variation with displacement / time)

Question 19

[Definition] Damped Oscillations

Answer 19

Damped oscillations are oscillations in which the amplitude decreases with time as a result of dissipative forces that reduces the total energy of the oscillations

Question 20

Light to Critical to Heavy Damping

Answer 20

Light to Critical to Heavy Damping:
Light: More time needed to return to equilbrium
Critical: Shortest possible time (no oscillation)
Heavy: More time than critical (no oscillation)

Question 21

[Definition] Forced Oscillations

Answer 21

Forced oscillations are oscillations where there is a continuous input of energy by an external periodic force that maintains the oscillation amplitude

Question 22

Amplitude - driving frequency graph

Answer 22

Increases from non-zero y-intercept to max (at natural frequency), then decreases to near zero

Question 23

[Definition] Resonance

Answer 23

Resonance is a phenomenon in which the amplitude of an oscillatory motion is at maximum because there is maximum rate of transfer of energy from the external driver to the oscillating system.

This occurs when the driving frequency of the external periodic force equals to the natural frequency.

Question 24

Amplitude - driving frequency graph of no damping to increased damping

Answer 24

1. Max amplitude decreases
2. Max amplitude shifts to left (cos period longer, so frequency decreases)
3. Flatter curve