What sets the period
▶︎ Watch it animatedinteractive step-through · ~3 min · optionalThe period of an oscillator is fixed by the system, not by how far it swings. For a block on a spring, T = 2π√(m/k): the period grows with the mass, shrinks with the stiffness, and does not depend on the amplitude or on how the motion is started.
The period hides three separate facts. It doesn't depend on amplitude: a wider swing is covered at a proportionally higher speed, so the round trip takes the same time. It does depend on mass and stiffness, but through a square root and in opposite directions, so heavier is slower and stiffer is faster. And the three rate quantities are linked by fixed factors of two pi — ω = 2πf and T = 2π/ω — so the 2π can never be dropped.
Frequency and period of SHM
3 ways in · any order
Lesson
Frequency and period of SHM
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What sets the period and frequency of an oscillator: the spring-mass relationship T equals two pi times the square root of mass over stiffness, why the period does not depend on the amplitude or the starting conditions, how it grows with the mass and shrinks with the stiffness through a square root, and how angular frequency, frequency, and period convert through factors of two pi. Closes with a ten-scenario skill check.
Diagnostic
10-item topic check
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Ten items across the three Topic 7.2 mistakes: assuming a larger amplitude changes the period, getting the mass and stiffness dependence backwards or mis-scaled in T equals two pi root m over k, and confusing angular frequency, frequency, and period by dropping or misplacing the factor of two pi. Take it cold to see what still trips you up, or after the lesson to confirm it does not.
Targeted Practice
Drill a single misconception
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Pick one mistake you keep making and drill it on its own. Two correct in a row clears it and you move on.