Welcome to Unit 7. Everything here is about periodic motion — motion that repeats itself at regular intervals: a swinging pendulum, a bouncing ball, a planet orbiting a star, a vibrating guitar string. But this unit zooms in on one particular kind of periodic motion that shows up constantly in physics and engineering: simple harmonic motion (SHM).
All five of these motions repeat — but only some of them are SHM. Pick one and check whether it passes the restoring-force test.
Notice what separates the SHM examples from the non-SHM ones: it isn't just whether the motion repeats. It's about the specific relationship between the force acting on the system and how far that system has moved from where it wants to sit at rest. That relationship is what the next section defines precisely.
SHM results when the magnitude of the restoring force exerted on an object is proportional to that object's displacement from its equilibrium position:
Drag the block away from equilibrium and watch the restoring force always point back toward it — growing with distance, per F = −kΔx (here, k = 2 N/m).
This is the same idea you first saw with an ideal spring back in earlier units — but here it's the definition of the entire category of motion, not just a spring-specific rule. Any system where the restoring force scales linearly with displacement, regardless of what's physically producing that force, exhibits SHM.
The restoring force condition only makes sense once you know what it's measured relative to. An equilibrium position is a location at which the net force exerted on an object or system is zero — the spot the system would stay at forever if it were placed there at rest, and the point every restoring force in SHM points back toward.
Test the SHM condition against five different force (or torque) laws. Only one thing matters: is the restoring force's magnitude directly proportional to displacement?
This classifying skill — checking a force or torque law against F = −kΔx before assuming SHM applies — is the foundation for the rest of Unit 7. Once you can confidently identify SHM, every equation for period, frequency, position, velocity, acceleration, and energy in the coming lessons becomes a tool you know exactly when to reach for.