10: Oscillations

Question 1

Periodic Motion

Answer 1

A periodic motion is one that repeats itself in equal intervals of time.

Question 2

R/s between period (T) and frequency (f)

Answer 2

T = 1/f

Question 3

Angular frequency, ω

definition

Answer 3

ω = 2πf = 2π/T

Question 4

Phase, θ

Answer 4

Phase is an angle (° or rad) which gives a measure of the fraction of a cycle that has been completed by an oscillating particle or wave.

Question 5

Phase difference, Φ

Answer 5

Phase difference is a measure of how much one wave is out of step with another.

Question 6

Simple Harmonic Motion (SHM)

Answer 6

SHM is the motion of a body whose acceleration is directly proportional to its displacement from a fixed point, and is always directed towards that point.

Question 7

Simple Harmonic Motion (SHM) equation

Answer 7

a ∝ -x

Question 8

Kinematics of SHM equations:

• x
• v
• a

Answer 8

• x = x₀ sin ωt
• v = v₀ cos ωt
• a = - ω² x

Question 9

Dynamics of SHM equations:

• ω
• a
• T

Answer 9

• ω = √(k/m)
• a = - (k/m) x
• T = 2π √(k/m)
• T = 2π √(L/g) (for simple pendulum)

Question 10

Energy of body in SHM:

• KE
• EPE
• Total E

Answer 10

• KE = 1/2 mω²(x₀² - x²)
• EPE = 1/2 mω²x²
• Total energy = 1/2 mω²x₀²

Question 11

Damped oscillations

Answer 11

Damped oscillations are oscillations in which the amplitude diminishes with time as a result of dissipative forces that reduce the total energy of the oscillation.

Question 12

Forced oscillations

Answer 12

A system is in forced oscillations when it is forced to oscillate at a frequency other than the natural frequency by a periodic external force.

Question 13

Resonance

Answer 13

Resonance is a phenomenon that occurs when the frequency at which an object is being made to vibrate is equal to its natural frequency of vibration.