Energy in oscillations and dampingEdexcel International A Level Physics: Subtopic test

1. 1
   A trolley of mass 0.40 kg is attached to a horizontal spring of spring constant 64 N m⁻¹. The trolley moves on a low-friction track, so the oscillations can be treated as undamped. It is pulled 0.050 m from its equilibrium position and released from rest.

   (a)

   Calculate the total energy of the oscillating system.

   [1 mark]

   • A0.16 J
   • B0.080 J
   • C1.6 J
   • D3.2 J

   (b)

   What is the maximum speed of the trolley?

   [1 mark]

   • A0.20 m s⁻¹
   • B0.45 m s⁻¹
   • C0.63 m s⁻¹
   • D0.89 m s⁻¹

   (c)

   Calculate the kinetic energy of the trolley when its displacement from equilibrium is 0.030 m.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   A pendulum has a bob of mass 0.15 kg on a light string. The bob is pulled aside until it is 0.040 m above its lowest position and released from rest. Air resistance is negligible for the first swing, but over several minutes the swings visibly become smaller.

   (a)

   Ignoring air resistance, what is the speed of the bob as it passes through its lowest position?

   [1 mark]

   • A0.89 m s⁻¹
   • B0.63 m s⁻¹
   • C0.78 m s⁻¹
   • D0.45 m s⁻¹

   (b)

   Which statement best describes the energy changes as the swings become smaller?

   [1 mark]

   • AEnergy is destroyed by air resistance
   • BThe maximum kinetic energy at the lowest position stays constant
   • CThe maximum gravitational potential energy of the bob increases
   • DMechanical energy is dissipated as thermal energy in the surroundings

   (c)

   Explain why the amplitude of the swings decreases with time.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A mass of 0.30 kg hangs from a spring and oscillates vertically with a period of 0.80 s and an initial amplitude of 6.0 cm. The mass is then lowered into a beaker of oil. In the oil the amplitude falls to 3.0 cm after a number of oscillations, and the period is unchanged.

   (a)

   Calculate the total energy of the oscillation before the mass is lowered into the oil.

   [3 marks]

   (b)

   Calculate the energy transferred away from the oscillation when the amplitude has fallen to 3.0 cm, and state what happens to this energy.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   A tall steel-framed building in an earthquake zone sways after the ground stops shaking. Its structural beams are made of ductile steel, which can yield plastically in a strong earthquake, and viscous dampers are fitted between floors. The effective mass of the building is 2.0 × 10⁶ kg. The top of the building oscillates at a frequency of 0.25 Hz with an amplitude of 0.12 m, and one cycle later the amplitude is 0.10 m.

   (a)

   Explain how the viscous dampers and the ductile steel beams cause the amplitude of the swaying to decrease.

   [6 marks]

   (b)

   Calculate the energy transferred away from the oscillation during this cycle, and express it as a percentage of the energy at the start of the cycle.

   [6 marks]

   Total for question 4: 12 marks

End of questions