Work, energy and momentum questions
Calculate work and power, conserve signed momentum and compare collision energies.
Simple harmonic motion questions
Calculate periods, signed acceleration, speed and energy; use the small-angle pendulum model.
Practise
Speed at a displacementAn object undergoes SHM with amplitude 2 cm and period 1.6 s. Find its speed at displacement -0.008 m from equilibrium. Give your answer to 3 significant figures.
Larger diagram
Treat the given values as exact unless an uncertainty is stated.
Hint
Use speed = ω√(A² − x²). Displacement alone does not specify velocity direction.
Worked solution
- A = 0.02 m; ω = 2π/1.6 rad s⁻¹.
- Speed = (2π/1.6) × √(0.02² − (-0.008)²) m s⁻¹.
- Answer: 0.0720 m s⁻¹ (3 significant figures).
Question type: Mixed practice
Report a problem
Displacement, velocity and acceleration
SHM is motion with acceleration proportional to displacement and directed towards equilibrium: a = −ω²x. Angular frequency ω = 2π/T = 2πf. A negative displacement gives a positive acceleration; it does not determine which way the object is moving.
Speed and energy
Speed = ω√(A² − x²), with A and x in metres. Maximum speed ωA occurs at equilibrium; speed is zero at the turning points. For an undamped oscillator, total oscillation energy relative to equilibrium is ½mω²A².
Spring and pendulum periods
A mass on a Hooke-law spring has T = 2π√(m/k), measured about its loaded equilibrium. A simple pendulum has T = 2π√(L/g) at small angles, where L runs from pivot to the bob’s centre. Use a light, inextensible string and a point-mass bob.
What this practice covers
Selected period, frequency, acceleration, speed, energy and model calculations. Damping, resonance, phase calculations and full practical methods are outside this set. Numerical answers use 3 significant figures; use the constants supplied in each question.
A-level relevance
AQA 7408: 3.6.1.2–3 (selected); OCR A H556: 5.3.1–2 (selected). Tasks cover the selected skills listed above.