8: Oscillations

Question 1

Define simple harmonic motion

Answer 1

SHM is a motion where
the acceleration is directly proportional to its displacement and
the direction of acceleration is always opposite of its displacement

Question 2

Imagine graph: (SHM)
1. Acceleration - displacement
2. Acceleration - time
3. Velocity - displacement
4. Energy - time
5. Energy - displacement

Answer 2

:’)

Question 3

Formula for KE and PE, KE max

Answer 3

KE = 1/2 x (m) x (w^2) x (xmax^2 - x^2)
PE = 1/2 x (m) x (w^2) x (x^2)

KE max = 1/2 x (m) x (w^2) x (x max ^2)

Question 4

What are the three types of forces that can exist in certain types of oscillations

Answer 4

Restoring Force
Resistive Force
Driving Force

Question 5

What is a free oscillation?

Answer 5

1. In free oscillation, there is only restoring force acting on the system
2. Total energy is always constant
3. Oscillation frequency = Natural Frequency

Question 6

What is Damped Oscillation

Answer 6

1. There are restoring and resistive force
2. System loses energy until object comes to a stop

Question 7

Imagine graphs:
1.Underdamped
2. Crticial damped
3. Over damped

Answer 7

1. Amplitude decreasing, period remains constant
2. Amplitude goes to zero before period
3. Amplitude goes to zero after period

Question 8

What is a Forced Oscillation

Answer 8

1. There must be a driving force provide by an external oscillator
2. Thus there is continuous energy input
3. System oscillated at frequency of driver

Question 9

Define Resonance

Answer 9

Resonance is the phenomenon in which there is maximum transfer of energy from driver to the oscillating system in a forced oscillation.

Question 10

Imagine graph of:
amplitude and frequency of driver
1. Whose amplitude is it?
2. Where does resonance occur?
3. How would the graph be affected when there is increased resistive force?
4. How would the graph be affected when there is a change in natural frequency?

Answer 10

1. Amplitude is of the oscillator
2. Resonance occurs where amplitude is max - max amplitude explains the largest energy transfer
3. The graph shifts down, however the peak remains at original resonant frequency
4. The graph shifts left/right, however peak amplitude remains the same