Oscillations

Question 1

What is displacement?

Answer 1

It is the instantaneous distance of moving object from its means position.

Question 2

What is amplitude?

Answer 2

It is the maximum displacement from the mean position

Question 3

What is time period?

Answer 3

It is the time taken for one complete oscillation

Question 4

What is frequency?

Answer 4

It is the number of oscillations per unit time

Question 5

What is angular frequency (omega)?

Answer 5

It is the rate of change of angular displacement.

(Omega) = 2(pi)f

Question 6

What is phase differences?

Answer 6

It is a measure of how much one wave is out of step with another wave

(Phi) = 2(pi)t/T

T is the time period and t is the time lag between the waves.

Question 7

What is simple harmonic motion?

Answer 7

It is the acceleration proportional to the displacement and directed towards a fixed point.

Question 8

What are the requirements for SHM?

Answer 8

1. Mass that oscillates
2. Position where the mass is in equilibrium
3. Restoring force that acts to return mass to equilibrium

Question 9

What is the formula for simple harmonic motion?

Answer 9

a = -(omega)^2 * x

Question 10

What does the negative sign in the equation of simple harmonic motion mean?

Answer 10

It represents that the a and x are in opposite directions - where a is always directed towards the mean position.

Question 11

What are the formulas for displacement in a simple harmonic motion?

Answer 11

X = Xo * sin(omega * t)

X = Xo * cos(omega * t)

Question 12

What is the formula for velocity?

Answer 12

V = +- (omega) (Xo^2 - x^2)^1/2

V = Vo * cos (omega * t)

V = - Vo * sin (omega * t)

Question 13

What is the formula for acceleration in a simple harmonic motion?

Answer 13

a = -(omega)^2 (x)

Can apply one of the 2 displacement equations.

Question 14

What is the derivation of the formula for kinetic energy?

Answer 14

V = +- (omega) (Xo^2 - x^2)^1/2

Substitute into

Ek = 1/2mv^2

Question 15

What is the formula for Potential energy in a simple harmonic motion?

Answer 15

Et = Ep + Ek

Ep = Et - Ek

Et = 1/2m(omega)^2*(x)^2

Question 16

What is damping?

Answer 16

It is the loss of energy and reduction in amplitude from an oscillating system caused by force acting in opposite direction to the motion.

Question 17

What is light damping?

Answer 17

System oscillates about equilibrium position with decreasing amplitude over a period of time.

Question 18

What is critical damping?

Answer 18

The system does not oscillate & is amount of damping required such that the system returns to its equilibrium position in the shortest possible time.

Question 19

What is the heavy damping?

Answer 19

The damping is so great that the displaced object never oscillates but returns to its equilibrium position very very slowly.

Question 20

Describe and example of oscillation and its damping in a car suspension.

Answer 20

The car oscillates due to spring like connections at the wheels.

Critical damping is needed in order to stop oscillation as quickly as possible to avoid motion sickness - hydraulic nature.

Question 21

Describe an example of oscillation in tall buildings and its oscillation.

Answer 21

The oscillation occurs during earthquakes.

A large weight is applied at the top of the building to supply a counter weight to counter the oscillation.

Question 22

What is the natural frequency of natural frequency?

Answer 22

It is the unforced frequency of oscillation of a freely oscillating object.

Question 23

What is free oscillation?

Answer 23

It is the oscillatory motion not subjected to an external periodic driving force - oscillating at natural frequency.

Question 24

What is forced oscillation?

Answer 24

It is oscillation that is caused by an external driving force; frequency is determined by the driving force.

Question 25

What is resonance?

Answer 25

It is the maximum amplitude of vibration when impressed frequency equals natural frequency’s of vibration.

Question 26

What is the effect of damping on the frequency and oscillation of an object undergoing forced damping?

Answer 26

1. Slight decrease in resonant frequency
2. Decrease if amplitude at all frequencies
3. Resonant eat becomes flatter.

Question 27

What are some examples of the useful purpose of resonance?

Answer 27

1. Oscillation of a child’s swing
2. Tuning of the radio receiver - the natural frequency of radio is adjusted so that it responds resonantly to a specific broadcast frequency.
3. Using a microwave to cook food - it produces a microwave of frequency equal to natural frequency of water that causes the water molecules in the food to vibrate to generate heat.
4. Magnetic resonance imaging is used in hospitals to create images of the humans organs.

Question 28

What are some examples of the destructive nature of oscillations?

Answer 28

High pitched objects can shatter fragile objects - like a glass when a soprano hits a high note

Buildings that vibrate at natural frequencies close to the natural frequency of seismic waves collapse during earthquakes

A car vibration system vibrates when going over bumps which would give large amplitude vibrations.

Question 29

Explain how a graph of maximum amplitude and frequency can be used to tell if an oscillation is damped or not.

Answer 29

If the peak is not sharp/ the peak is not of infinite height, then it will be damped.

Question 30

State an application for Resonance.

Answer 30

1. Quartz crystal to produce the ultrasound
2. (quartz crystal) in watch to keep timing
3. NMR/ MRI
4. Microwave ovens
5. Tuning circuits.