Physics

1. 1.

   An oscillator executes simple harmonic motion (SHM) with angular frequency 5.0 rad s^-1. Calculate acceleration at displacement +0.080 m from equilibrium and explain the sign.

   [3 marks]
2. 2.

   A mass 0.250 kg oscillates on a spring of stiffness 40.0 N m^-1. Find the period. Assume a massless spring and negligible damping.

   [3 marks]
3. 3.

   A 0.200 kg oscillator executes simple harmonic motion (SHM) with amplitude 0.0500 m and omega = 10.0 rad s^-1. Find its speed and kinetic energy when its displacement from equilibrium is x = 0.0300 m. Neglect damping.

   [3 marks]
4. 4.

   An SHM displacement is x = 0.0400cos(4.00t) m, with t in seconds. Find the first positive time at which x = 0.0200 m and the signed velocity then, to 3 significant figures.

   [3 marks]
5. 5.

   A pendulum has length 0.800 m and small amplitude. After moving to a location with unknown g its measured time for 20 complete periods is 36.0 s. Estimate g and its percentage uncertainty if total timing uncertainty is +/-0.2 s and length uncertainty +/-0.005 m. Use a worst-case first-order uncertainty sum.

   [4 marks]
6. 6.

   For weak damping the amplitude envelope is A(t) = A0 e^(-0.120t), with t in seconds and constant oscillator stiffness. Using a slowly varying envelope model in which cycle-averaged mechanical energy is approximately proportional to A^2, find the approximate time for that energy to fall to one quarter of its initial value. Explain why maximum forced-response amplitude need not occur exactly at the undamped natural frequency.

   [3 marks]

Original, unofficial practice questions from SubjectScout — not official past-paper questions.