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
Oscillator energyA 0.2 kg object undergoes undamped SHM with period 1.2 s and amplitude 4 cm. Calculate its total oscillation energy, taking potential energy as zero at equilibrium. Give your answer to 3 significant figures.
Treat the given values as exact unless an uncertainty is stated.
Hint
At equilibrium all oscillation energy is kinetic: E = ½m(ωA)².
Worked solution
- E = ½ × 0.2 × (2π/1.2)² × 0.04² J.
- This is energy relative to equilibrium, not the absolute gravitational or spring energy.
- Answer: 4.39 × 10-3 J (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.