Further Mechanics

Question 1

What is the condition for SHM?

Answer 1

An oscillation in which the acceleration of an object is directly proportional to its displacement from the midpoint, and is directed towards the midpoint:

a ∝ -x

Question 2

What is the defining equation for SHM?

Answer 2

a = -ω²x

Question 3

What is the relationship between frequency and amplitude and time period and amplitude?

Answer 3

Both are independent of amplitude.

Question 4

What effect does damping have on oscillations?

Answer 4

• Reduces amplitude over time
• The heavier the damping, the quicker the amplitude is reduced (the tighter the envelope)
• Critical damping reduces the amplitude to zero in the shortest possible time.
• Over damping doesn’t allow any oscillation past the eqm. point but causes a slower return to eqm. than a critically damped system.

Question 5

What are free and forced vibrations?

Answer 5

• Free:
  
  • no energy transferred to or from surroundings
  • object always oscillates at resosnant frequency
• Forced:
  
  • periodic external force applied to object to force it to vibrate
  • frequncy of force is called driving frequency
  • if driving frequency is much less than the resonant freq., the force and oscillator will be in phase
  • if driving freq. is much higher than the resonant freq., the oscillator can’t keep up and the driver is out of phase with the oscillator.

Question 6

What is the effect of damping on resonance?

Answer 6

• light damping = sharp resonance peak ( amplitude only increases dramatically when the driving freq. is v. close to the resonant freq.
• heavy damping = flatter curve: amplitude doesnt increase as much but drop off is more gradual

Question 7

Draw a graph showing how the amplitude of a system varies with driving freq. when it is lightly damped and heavily damped.

Answer 7

Question 8

Explain how damping is used to improve sound quality in enclosed spaces.

Answer 8

When certain frequencies of soundwaves are reflected off of the walls of a room, stationary waves are formed, causing resonance, which affects the quality of the sound (these frequencies are louder than they should be). Soundproofing foam is used to absorb the sound energy, damping the oscillations of these frequencies so that the amplitude doesn’t increase as much due to resonance.