A Level · A2 · structured
A Level extension · Question 9
A Level extension · Original GioPhysics question with a detailed, mark-by-mark answer guide.
- Demand
- demanding
- Marks
- 12
- Topics
- 1
- Answer
- Complete
A mass suspended from a spring oscillates vertically with simple harmonic motion of amplitude 4.0 cm and period 0.80 s.
- (a)
Define Define simple harmonic motion.
2 marks - (b)
Calculate Calculate the maximum speed of the mass.
3 marks - (c)
Calculate Calculate the speed of the mass when its displacement from the equilibrium position is 2.0 cm.
3 marks - (d)
Explain The mass is now made to oscillate by a driver whose frequency can be varied, and the system is lightly damped. Describe how the amplitude of the oscillations varies with the driving frequency, and explain what happens to the response curve if the damping is increased.
4 marks
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(a)
Define Define simple harmonic motion.
Identify what the question is testing, organise the response into distinct mark-earning points, and make every conclusion traceable to a physical principle or to the evidence supplied.
- 1
motion in which the acceleration is proportional to the displacement from a fixed point
- 2
and is always directed towards that point (opposite in direction to the displacement)
(b)
Calculate Calculate the maximum speed of the mass.
List the given quantities with units, identify the required quantity, write the governing relationship before substituting, and keep extra digits until the final line so rounding does not distort the result.
- 1
ω = 2π/T = 2π/0.80 = 7.85 rad s⁻¹
- 2
v_max = ωx₀ = 7.85 × 0.040
- 3
v_max = 0.31 m s⁻¹
(c)
Calculate Calculate the speed of the mass when its displacement from the equilibrium position is 2.0 cm.
List the given quantities with units, identify the required quantity, write the governing relationship before substituting, and keep extra digits until the final line so rounding does not distort the result.
- 1
v = ω√(x₀² − x²)
- 2
v = 7.85 × √(0.040² − 0.020²) = 7.85 × 0.0346
- 3
v = 0.27 m s⁻¹
(d)
Explain The mass is now made to oscillate by a driver whose frequency can be varied, and the system is lightly damped. Describe how the amplitude of the oscillations varies with the driving frequency, and explain what happens to the response curve if the damping is increased.
State the outcome first, then link cause to effect with the relevant physical principle. Each link in the reasoning should be explicit enough to earn its own marking point.
- 1
the amplitude is small at low driving frequencies, rises to a sharp maximum when the driving frequency equals the natural frequency of the system, then falls again
- 2
this maximum is resonance, and at it the driver transfers energy to the system most efficiently
- 3
increasing the damping lowers the peak amplitude and makes the peak broader (flatter)
- 4
and the peak occurs at a slightly lower frequency than the undamped natural frequency
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