5.3 Oscillations

Question 1

provide and explain the defining equation for simple harmonic motion

Answer 1

a=-ω²x
acceleration ∝ to the displacement from the midpoint, directed towards the midpoint

Question 2

define amplitude, frequency and period

Answer 2

amplitude: points of extreme motion
frequency: no. cycles per second
period: time taken for one complete cycle
f=1/t, t=1/f

Question 3

define the term isochronous oscillator

Answer 3

the period is independent of the amplitude (all objects in SHM are isochronous oscillators)

Question 4

recall the equations for displacement in SHM and when to use each one

Answer 4

x=Acosωt, x=Asinωt
where cosine is used if the time starts at max displacement, and sine if it starts at equilibrium.

Question 5

recall the equations for velocity in SHM

Answer 5

v=±ω√(A²-x²), v(max)=ωA

Question 6

recall the equations for acceleration in SHM

Answer 6

a=-ω²x, a(max)=ω²A

Question 7

explain phase difference, and in phase and antiphase waves

Answer 7

phase difference=lag, measured in radians/degrees/fractions of a cycle
in phase: phase difference of zero or 360°, 720°, 2π rad, 4π rad etc.
antiphase: phase difference of 180°, π rad, etc.

Question 8

describe the relationship between KE and PE in SHM

Answer 8

KE and PE are in antiphase, most PE at the beginning of the motion, most KE at rest position (neither can be negative)

Question 9

describe free and forced oscillations

Answer 9

free oscillations: no energy transfer to/from surroundings, if no energy is transferred it will oscillate forever (e.g. plucking guitar string, oscillates at natural frequency)
forced oscillations: external driving force in system, frequency=driving frequency

Question 10

explain resonance and provide examples

Answer 10

resonance: as driving frequency → natural frequency, system gains more energy from driving frequency ∴ amplitude rapidly increases
examples: radio tuning, glass shattering, string instruments

Question 11

explain damping and provide an example

Answer 11

oscillation loses energy to surroundings (eg. doing work to overcome effects of air resistance or friction)
systems often deliberately damped to minimise effects of resonance

Question 12

explain the different degrees of damping

Answer 12

light damping (takes longer amount of time to return to equilibrium)
critical damping (shortest amount of time to return to equilibrium)
over-damping (takes longer amount of time to return to equilibrium, slower than light damping)

Question 13

provide examples of practical damping

Answer 13

car suspension systems are often critically damped to reduce oscillations, and heavy doors are often overdamped
designing buildings to withstand earthquakes via tuned mass damping (pendulum moves opposite to building movement) (critical damping)