Six original Cambridge-style questions on the defining condition a = −ω²x, the equations x = x₀ sin ωt and v = ±ω√(x₀² − x²), and how the three graphs line up.
A ball dropped onto a hard floor bounces repeatedly, rising to the same height each time. State the condition that must be met for a motion to be simple harmonic, and explain why the bouncing ball does not satisfy it.
The piston of a small engine moves with simple harmonic motion of amplitude 45 mm while the crankshaft turns at 3000 revolutions per minute. Calculate the angular frequency of the motion, the maximum speed of the piston, and its maximum acceleration.
A buoy bobs up and down on the sea with simple harmonic motion of amplitude 0.60 m and period 4.0 s. At time t = 0 it passes through its equilibrium position moving upwards. Calculate its displacement and its velocity at t = 0.50 s.
The displacement-time graph of an object in simple harmonic motion is a sine curve. Describe how the velocity-time graph and the acceleration-time graph of the same motion are related to it, and state the displacement at which the velocity and the acceleration each have their greatest magnitude.
An object oscillates with simple harmonic motion about a fixed point. Its speed is 0.24 m s⁻¹ when its displacement is 30 mm and 0.18 m s⁻¹ when its displacement is 40 mm. Determine the amplitude and the angular frequency of the motion.
A loudspeaker cone vibrates with simple harmonic motion at a frequency of 250 Hz and an amplitude of 0.80 mm.
(a) Calculate the angular frequency of the motion. (b) Calculate the maximum acceleration of the cone. (c) Determine the displacement of the cone at the instants when its speed is half its maximum value.
Mark this once you have attempted all six and checked your working. It records a Practiced badge on the topic and adds a one-time bonus. Revealing the solutions alone does not count.