Ch17 simple harmonic motion

Question 1

What are the 2 conditions for simple harmonic motion?

Answer 1

• acceleration of the object is proportional to displacement
  F=kx
  ma=kx
  a= k/m X x
• acceleration is always directed towards equilibrium:
  negative gradient, acceleration and displacement in opposite directions

Question 2

displacement equations in simple harmonic motion.

Answer 2

x=Acos(wt) when oscillating object start from maximum displacement
x=Asin(wt) when oscillating object start from zero displacement

Question 3

What are the graphs in simple harmonic motion?

Answer 3

displacement against time:
cos graph
velocity against time:
-sin graph
acceleration against time:
-cos graph

Question 4

Velocity in simple harmonic motion

Answer 4

x=-A x=0 x=A

V= +-w √A^2-x^2

When x=A
V=0
When x=-A
V=0
When x=0
V is max

Vmax=wA

Question 5

kinetic energy in energy against displacement graph:

Answer 5

x=A x=0 x=-A

at x=A and x=-A:
kinetic energy = 0
at x=0:
kinetic energy = max

Question 6

potential energy in energy graph against displacement

Answer 6

x=A x=0 x=-A
at x=A and x=-A:
potential energy = max
at x=0:
potential energy=0

Question 7

Period dependence on amplitude experiments.
equipment:

Answer 7

-stand
-mass
-spring
-stop clock
-fiducial marker, which is an object placed in the field of view to be used as a reference point.

Question 8

Period dependence on amplitude experiments.
procedure:

Answer 8

-place fiducial marker at equilibrium
-measure original length of the spring
-measure length of the spring before realising it (this length is the amplitude)
-release the spring to initiate SHM
-time 10 oscillation to reduce uncertainty
- divide by 10 to get 1 time period
- repeat with multiple amplitude

Question 9

Period dependence on amplitude experiments.
conclusion:

Answer 9

in SHM, time period is independent of amplitude.

Question 10

Natural frequency

Answer 10

The frequency at which an object oscillates after an initial disturbance

Question 11

Driving frequency

Answer 11

When a driver forces an object to oscillate at a frequency different to its natural frequency

Question 12

Resonance

Answer 12

• Resonance is a driving force, same direction as velocity.
• increase the amplitude.
• Resonance occurs when driving frequency matches the natural frequency.
  Effects:
• max energy transfer from driving force to the system
• oscillation reach maximum amplitude.

Question 13

Damping

Answer 13

Damping is a resistive force that acts opposite to direction of motion/velocity.
Effects:
- amplitude decreases.
- time period remains the same, remember in SHM the time period is independent of the amplitude.