Energy, damping and resonanceEdexcel A-Level Physics: Subtopic test

1. 1
   A trolley of mass 0.50 kg is held between two identical springs on a horizontal, frictionless track. It is pulled aside and released, and then oscillates with simple harmonic motion with amplitude 0.060 m and period 1.2 s. Air resistance is negligible.

   (a)

   Which statement correctly describes the energy of the trolley as it moves from maximum displacement to the equilibrium position?

   [1 mark]

   • AElastic potential energy is transferred to kinetic energy and the total energy stays constant
   • BKinetic energy is transferred to elastic potential energy and the total energy stays constant
   • CElastic potential energy is transferred to kinetic energy and the total energy decreases
   • DKinetic energy and elastic potential energy both increase

   (b)

   The trolley passes the point where its displacement from equilibrium is 0.030 m. What fraction of its total energy is kinetic at this point?

   [1 mark]

   • A$\frac{1}{4}$
   • B$\frac{1}{2}$
   • C$\frac{3}{4}$
   • DAll of it

   (c)

   Calculate the maximum kinetic energy of the trolley.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   The drum of a washing machine is mounted on springs and has a natural frequency of vibration of 8.0 Hz. During the spin cycle the motor speed increases steadily from 0 to 20 Hz, so the drum is driven by a periodic force at the spin frequency.

   (a)

   At which spin frequency is the amplitude of vibration of the drum greatest?

   [1 mark]

   • A20 Hz
   • B4.0 Hz
   • C16 Hz
   • D8.0 Hz

   (b)

   When the drum is spinning steadily at 20 Hz, which statement describes its motion?

   [1 mark]

   • AA free oscillation at 8.0 Hz
   • BA forced oscillation at 20 Hz
   • CA forced oscillation at 8.0 Hz
   • DA free oscillation at 20 Hz

   (c)

   Explain why the vibrations of the drum become very large as the spin frequency approaches 8.0 Hz.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   The body of a car on its suspension behaves as a mass on springs with a natural frequency of 1.5 Hz. The car is fitted with oil-filled shock absorbers. It is driven along a road with evenly spaced ridges, and at one particular speed the ridges push the car upwards 1.5 times every second.

   (a)

   The car hits a single bump and its body oscillates vertically. Explain what happens to the amplitude and to the total mechanical energy of the oscillation as the shock absorbers act.

   [3 marks]

   (b)

   Suggest why the car is fitted with heavily damped shock absorbers, with reference to resonance and the effect of damping on the amplitude of a forced oscillation.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   Students hang known masses from a vertical spring and measure the period T of small vertical oscillations. Their straight-line graph of T² against mass m passes through the points (0.050 kg, 0.30 s²) and (0.150 kg, 0.70 s²). They then hang an unknown mass from the same spring and find that its period is 0.90 s.

   (a)

   Use the graph points to determine the spring constant of the spring, and the value of the unknown mass. Use $T^2 = \frac{4\pi^2}{k} m + c$.

   [6 marks]

   (b)

   Describe how the students should carry out the experiment to obtain reliable values of T, and explain why the line does not pass through the origin.

   [6 marks]

   Total for question 4: 12 marks

End of questions