Energy and SHM

Question 1

What is the kinetic energy of a oscillating mass?

Answer 1

E_K = E_T - E_P

= ½k(A²-x²)

Question 2

Derive the velocity of SHM

Answer 2

• EK = ½mv² = ½k(A² - x²)
• As ω² = k/m.
• Therefore v^{<span>2</span>} = ω²(A² - x²)
• So v = ±ω²(A² - x²)

Question 3

Describe the energy displacement graph

Answer 3

• Elastic potential energy maximum at extremities and equals kA². Curve is a parabola.
• Kinetic energy maximum at displacement = 0. Curve is an inverted parabola.
• Total energy of a pendulum = sum of kinetic and gravitational potential energies.
• Total energy is constant giving a horizontal line on the graph.

Question 4

What are damped oscillations?

Answer 4

Oscillations that reduce in amplitude due to the presence of resistive/dissipative forces such as friction and drag.

Question 5

What happens to the energy in damped oscillations?

Answer 5

It is dissipated into the sourroundings as thermal energy.

Question 6

When does light dampening occur?

Answer 6

Light dampening occurs when the time period is independent of the amplitude so each cycle takes the same length of time as the oscillations die away.

Question 7

What is critical damping?

Answer 7

Enough dampening for the system to return to the equilibrium after being displaced in the least possible time without oscillating.

Question 8

When does heavy dampening occur?

Answer 8

Heavy dampening ocurrs when the dampening is so strong that the displaced object slowly returns to equilibrium without oscillating.