5.3 Oscillations

Question 1

What is angular frequency?

Answer 1

• The rate of change of angular displacement
• ω=2π/T=2πf

Question 2

What is simple harmonic motion?

Answer 2

• The acceleration of the object is directly proportional to its displacement
• The acceleration of the object acts in the opposite direction to the displacement (always in the direction of the equilibrium position)
• Defining equation is a=-xω^2

Question 3

What is a fiducial marker?

Answer 3

• A marker placed at the equilibrium position in an SHM experiment to provide a clear point from which to start and stop timing measurements

Question 4

When should you use x=Acosωt?

Answer 4

• When the oscillator begins at its amplitude (e.g. a pendulum starts swinging from a point above the equilibrium point)
• Always use calculator in radians!

Question 5

When should you use x=Asinωt?

Answer 5

• When the oscillator begins at its equilibrium point (e.g. a pendulum is flicked from its equilibrium point)
• Always use calculator in radians!

Question 6

How do you draw a v-t or a-t graph from an x-t graph?

Answer 6

• differentiate the x-t graph to get the v-t graph and differentiate the v-t graph to get the a-t graph
• e.g. if the x-t graph is a cosine graph, the v-t graph will be a -sin graph and the a-t graph will be a -cos graph.

Question 7

What equation governs velocity of SHM and how does this apply to maximum velocity?

Answer 7

• v=ω√A^2-x^2
• At maximum velocity, the displacement is zero (mass is at equilibrium point), so vmax=ωA

Question 8

What does isochronous mean?

Answer 8

• The time period of an oscillator is independent of its amplitude

Question 9

What is a free oscillation?

Answer 9

• A system is displaced from its equilibrium position initially, then allowed to oscillate with no external forces applied
• The frequency is called the natural frequency

Question 10

What is a forced oscillation?

Answer 10

• A driving force is applied during the oscillation
• The frequency is called the driving frequency

Question 11

What changes when damping is applied to a system?

Answer 11

• amplitude decreases
• period and frequency remain the same
• maximum speed decreases

Question 12

When does resonance occur?

Answer 12

• The driving frequency of a forced oscillation is equal to the natural frequency of the oscillator (assuming there is negligible damping on the driving force)
• The amplitude increases greatly

Question 13

What changes on an amplitude-driving frequency graph when damping is applied?

Answer 13

• The peak was originally at the natural frequency
• As damping increases, the peak gets smaller and shifts towards the left