Practice
Simple harmonic motion
Periods of springs and pendulums, frequency, position at a given time, and the energy and greatest speed of a spring oscillator.
The skill
For a block on an ideal spring the period is ; for a simple pendulum at a small angle it is , and frequency is . Energy answers the other questions: at the turning points all of it is in the spring, , and at equilibrium it is all kinetic, so the speed is greatest there. Students often expect a bigger amplitude to change the period. It does not; it changes the energy.
A worked example
A 1.0 kg block on a level, frictionless surface is attached to an ideal spring with spring constant 280 N/m.
It is pulled aside and released. What is the period of its oscillation, in seconds? Give your answer to three significant figures.
Solution
- Tₛ = 2π√(m/k) = 2π√(1.0 ÷ 280) = 0.375 s.
- The amplitude does not appear: a bigger pull gives a faster trip over a longer path, in the same time.
Answer: 0.375