1. 1
   A mass of 0.40 kg hangs from a light spring of spring constant 25 N m⁻¹. The mass is pulled 3.0 cm below its equilibrium position and released, and it oscillates vertically with simple harmonic motion.

   (a)

   What is the time period of the oscillation?

   [1 mark]

   • A0.13 s
   • B0.79 s
   • C1.3 s
   • D50 s

   (b)

   What is the magnitude of the maximum acceleration of the mass?

   [1 mark]

   • A0.75 m s⁻²
   • B190 m s⁻²
   • C1.9 m s⁻²
   • D9.8 m s⁻²

   (c)

   The 0.40 kg mass is replaced by a 1.6 kg mass on the same spring. Deduce the new frequency of oscillation.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   A student makes a simple pendulum from a small, dense bob on a light, inextensible string. With the string length set to 0.800 m, she displaces the bob through a small angle, releases it, and times 20 complete oscillations with a hand-held stopwatch. The time recorded is 35.9 s.

   (a)

   Why must the bob be displaced through only a small angle for its motion to be simple harmonic?

   [1 mark]

   • ASo that air resistance is zero
   • BSo that the tension in the string is constant
   • CSo that the period depends on the mass of the bob
   • DSo that the restoring force is approximately proportional to the displacement

   (b)

   What value of the acceleration due to gravity does the student obtain?

   [1 mark]

   • A9.80 m s⁻²
   • B1.56 m s⁻²
   • C39.2 m s⁻²
   • D0.0245 m s⁻²

   (c)

   Explain why timing 20 oscillations, rather than a single oscillation, improves the reliability of the value of g.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A glider of mass 0.25 kg on a horizontal air track is attached between two stretched springs fixed to the ends of the track. A sensor records the glider's displacement from the centre of the track and its acceleration. At a displacement of +4.0 cm the acceleration is −1.6 m s⁻²; at −2.0 cm it is +0.80 m s⁻²; at +1.0 cm it is −0.40 m s⁻².

   (a)

   Show that the data are consistent with the glider moving with simple harmonic motion, and determine its time period.

   [3 marks]

   (b)

   The air supply is reduced so that a small friction force acts on the glider. Describe the energy changes during one oscillation that starts at maximum displacement, and suggest how the amplitude and time period are affected by the friction.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   The body of a car has a mass of 1200 kg and is supported by four suspension springs that together act as a single spring of stiffness 6.0 × 10⁴ N m⁻¹. Shock absorbers fitted alongside the springs remove energy from any vertical oscillation. Four passengers with a total mass of 300 kg then get into the car.

   (a)

   Explain the conditions required for simple harmonic motion and discuss the extent to which the vertical motion of the car body can be modelled as simple harmonic motion.

   [6 marks]

   (b)

   Determine the frequency of vertical oscillation of the car body with and without the passengers, and evaluate the claim that adding the passengers makes the car bounce at a noticeably lower frequency.

   [6 marks]

   Total for question 4: 12 marks

End of questions