Amplitude, Period, and Frequency
A short lesson with diagrams, a worked example, a problem to try, and a quick check. Then quiz yourself on 5 practice questions.
Three numbers describe an oscillation. Amplitude A: the farthest it gets from equilibrium. Period T: the time for one full cycle. Frequency f: cycles per second, f = 1/T. For SHM, the period doesn’t depend on the amplitude.
1. Reading them off a graph
2. Period vs. amplitude
Pull a mass on a spring out farther and it has farther to go, but the bigger force also makes it move faster. The two effects cancel exactly: the period stays the same.
That’s why a pendulum clock keeps time even as its swing slowly shrinks.
A full cycle means back to the same position moving the same direction. From one end to the other end is only half a period; from equilibrium to an end is a quarter period.
3. Example, then try it
A mass on a spring completes 30 cycles in 12 s. Find its period and frequency.
T = 12 s ÷ 30 = 0.40 s. f = 1/T = 1 ÷ 0.40 = 2.5 Hz (or 30 ÷ 12).
A mass oscillates with amplitude 5.0 cm and completes 10 cycles in 4.0 s. Find T and f. How far does it travel in one period? In 2.0 s?
Period: T = 4.0 ÷ 10 = 0.40 s; f = 1 ÷ 0.40 = 2.5 Hz.
One period: out to one end, back, out to the other end, back: 4A = 4(5.0) = 20 cm.
In 2.0 s: 2.0 ÷ 0.40 = 5 cycles, so 5 × 20 cm = 100 cm = 1.0 m.
Bonus: after 5 whole cycles, it’s back where it started, so its displacement is zero.
Answer: T = 0.40 s, f = 2.5 Hz; 20 cm per period; 1.0 m in 2.0 s.
4. Common mistakes
A mass on a spring is pulled out twice as far before being released. What happens to its period?
In SHM the period doesn’t depend on the amplitude. The mass travels farther but also moves faster, and the effects cancel.
Ready to practice?
5 questions on Amplitude, Period, and Frequency, each with a hint and an explanation for every wrong answer.