What makes it simple harmonic
▶︎ Watch it animatedinteractive step-through · ~3 min · optionalSimple harmonic motion has one defining rule: the acceleration is proportional to the displacement and points the opposite way, a = −ω²x. That single relationship, restoring, linear, and through the origin, is what separates an oscillator from every other back-and-forth motion.
Everything turns on telling true simple harmonic motion from motion that merely repeats. The minus sign is essential: drop it and the motion runs away instead of oscillating. The acceleration is never constant — largest at the turning points, zero at the center — so constant-acceleration kinematics does not apply. And a restoring force alone isn't enough; it must be linear in the displacement, F = −kx. A bouncing ball or a wide-swinging pendulum repeats without ever being simple harmonic.
Defining simple harmonic motion
3 ways in · any order
Lesson
Defining simple harmonic motion
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What defines simple harmonic motion: the relationship a equals negative omega squared times x, why the minus sign makes the acceleration restoring, why the acceleration is not constant but largest at the ends and zero at the center, and why the force must be linear in the displacement, F equals negative k x. Sorts true SHM from motion that is merely periodic. Closes with a ten-scenario skill check.
Diagnostic
10-item topic check
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Ten items across the three Topic 7.1 mistakes: dropping the minus sign so the acceleration points the same way as the displacement, treating the acceleration as constant and reaching for constant-acceleration kinematics, and assuming any restoring force is simple harmonic when the force must be linear in the displacement. 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.