Chapter 14 - Periodic Motion

Question 1

What is periodic motion?

Answer 1

Motion that repeats itself in an indefinite cycle.

Question 2

When does periodic motion occur?

Answer 2

Whenever a body has a stable equilibrium position and restoring force that acts when the body is displace from equilibrium.

Question 3

What is the period?

Answer 3

T

Time for one cycle.

Question 4

What is frequency?

Answer 4

f

Number of cycles per unit time.

Question 5

What is angular frequency?

Answer 5

Omega

2pi*f

Question 6

Formula for angular frequency:

Answer 6

Omega = 2pi*f = 2pi/T

Question 7

What is Simple Harmonic Motion? SHM

Answer 7

When the restoring force F_x in periodic motion is directly proportional to the displacement x, the motion is called SHM.

Question 8

In SHM, what depends on mass m and force constant k?

Answer 8

Nothing depends on amplitude.

Angular frequency
Frequency
Period in SHM

Question 9

Which features of SHM are sinusoidal functions of time?

Answer 9

Displacement
Velocity
Acceleration in SHM

Question 10

What are the Amplitude A and phase angle of the oscillation determined by?

Answer 10

Initial displacement

Velocity of the body

Question 11

Formula for displacement?

Answer 11

x= Acos(omega*t + phase angle)

Question 12

Energy is conserved in SHM, the total energy can be expressed in terms of?

Answer 12

Force constant k and amplitude A

E=0.5mv^2 + 0.5kx^2 = 0.5kA^2 = constant

Question 13

In angular SHM the frequency and angular frequency are related to:

Answer 13

The moment of inertia

Torsion constant k

Question 14

Formulas for angular SHM:

Answer 14

Omega = Sqrt(torsion constant/inertia)
Frequency = 1/2pi Sqrt(torsion/inertia)

Question 15

A simple pendulum consists of:

Answer 15

Point mass m at the end of a massless string of length L.

Question 16

In a simple pendulum, what does the angular frequency, frequency and period depend on?

Answer 16

g and L

Question 17

What is a physical pendulum?

Answer 17

Any body suspended from an axis of rotation.

Question 18

In a physical pendulum what is the angular frequency and period for small amplitude oscillations dependant on?

Answer 18

Mass
Distance from the axis of rotation to the centre of gravity
Moment of inertia

Question 19

Formulas for a physical pendulum:

Answer 19

Angular frequency = Sqrt (mgd/I)

Period = 2pi*above

Question 20

What causes a damped oscillation?

Answer 20

When a force F =-bv is added to a simple harmonic oscillator.

Question 21

If b < 2SQRT(km)

Answer 21

Underdamping
The system oscillated with a decaying amplitude and an angular frequency (omega dashed) that it lower than it would be without damping.

Question 22

If b= 2SQRT(km)

Or b>2SQRT(km)

Answer 22

Critical damping
Or Over damping
When the system is displaced it returns to equilibrium without oscillating.

Question 23

What is forced/driven oscillation?

Answer 23

When a sinusoidally varying driving force is added to a damped harmonic oscillator.

Question 24

What is resonance in driven oscillations?

Answer 24

The amplitude is a function of the driving frequency and reaches a peak at the driving frequency close to the natural frequency of the system. This behaviour is resonance.