Simple harmonic motion

Question 1

What is damping?

Answer 1

• The reduction in energy and amplitude of oscillations due to resistive forces on the oscillating system

Question 2

What happens to the oscillations due to damping?

Answer 2

• The oscillators will rapidly, or gradually come to a rest
• The frequency of the oscillations does not change, only the amplitude decreases
• Hence, the time period remains the same

Question 3

What are the three types of damping?

Answer 3

• Light damping
• Critical damping
• Heavy damping

Question 4

What happens during light damping?

Answer 4

• The amplitude does not decrease linearly, but rather decays exponentially over time
• When a lightly damped oscillator is displaced from the equilibrium, it will oscillate with a decreasing amplitude

Question 5

What happens during critical damping?

Answer 5

• When a critically damped oscillator is displaced from the equillibrium, it will return to rest at its equillibrium position in the shortes possible time without oscillating
• The system does not oscillate, hence the displacement falls straight to 0

Question 6

What happens during heavy damping?

Answer 6

• When a heavily damped oscillator is displaced from the equillibrium, it will take a long time to return to its equillibrium position without oscillating
• There’s no oscillations so displacement does not pass 0
• The graph has a slow decreasing gradient

Question 7

What are free oscillations?

Answer 7

• Free oscillations occur when there is no transfer of energy to or from the surroundings
• This happens when an oscillating system is displaced and then left to oscillate
• A free vibrations always oscillates at its resonant frequency

Question 8

What are forced oscillations?

Answer 8

• Oscillations acted on by a periodic external force where energy is given in order to sustain oscillations
• This periodic force does work against the resistive force responsible for decreasing the oscillations

Question 9

What is the natural frequency of an oscillating system?

Answer 9

• The frequency of an oscillation when the oscillating system is allowed to oscillate freely

Question 10

What is resonance?

Answer 10

• When the frequency of the applied force to an oscillating system is equal to its natural frequency, the amplitude of the resulting oscillation inscreases significantly

Question 11

Why is amplitude at its maximum at resonance?

Answer 11

• Energy is transferred from the driver to the oscillating system most efficiently
• Therefore, the system will be transferring maximum kinetic energy

Question 12

How does damping effect resonance?

Answer 12

• Damping reduces the amplitude of resonance vibrations

Question 13

What are the conditions for simple harmonic motion?

Answer 13

• There is repetitive back and forth movement through an equilibrium
• The time period of each complete vibration is the same
• The force responsible for the motion is always directed towards the equilibrium and is directly proportional to the distance from it

Question 14

When is an oscillation said to have SHM?

Answer 14

• The acceleration is directly proportional to the displacement
• The acceleration acts in the opposite direction to the displacement

Question 15

How do you calculate the acceleration of an object oscillating with SHM?

Answer 15

• acceleration = - angular velocity squared x displacement
• a = −⍵^2 * x