Spring Forces
Stretch a spring or push it in, and it pushes back. The size of the push scales with how far you have moved the spring from its relaxed length: $|F_s| = k|x|$, where $x$ is the displacement from equilibrium and $k$ is the spring constant. The direction always points back toward equilibrium, which is why $F_s$ is called a restoring force. A stiffer spring (large $k$) pushes harder for the same stretch.
Two pitfalls. At a turning point of an oscillation the velocity is zero, and students conclude the acceleration must be zero too. But the spring force is at its maximum there, and so is the acceleration. And students often treat a negative spring force as no force at all, when the negative sign is just shorthand for "points the other way." The lesson walks both.
The work
3 ways in · any order
Lesson
Spring Forces
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Read the lesson. Two worked examples (spring constant from equilibrium stretch, acceleration at the instant of release) followed by a ten-scenario applet that drills the always-toward-equilibrium direction, the turning-point trap, and the proportional-not-constant force.
Diagnostic
10-item topic check
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Ten multiple-choice items on Hooke's law, the always-toward-equilibrium direction rule, and the turning-point misread where zero velocity is mistaken for zero acceleration.
Targeted Practice
Drill a single misconception
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Pick one of the failure modes you've missed and grind it on its own. The round is adaptive: two correct in a row clears the misconception and you move on.