Restoring force
● VERBATIM — examined word-for-wordThe net force on the body that is always directed towards the equilibrium position, acting to restore it there. F–x graph: straight line through the origin, negative gradient. Describing it (4-mark N2016 pattern): pendulum — the component of the weight along the arc, towards the lowest point; floating object — displaced down, upthrust exceeds weight (net up); displaced up, weight exceeds upthrust (net down).
F = −kx · F = ma = −mω²xWhat this actually means
The restoring force is the net force that always points back to equilibrium. Its F–x graph is a straight line through the origin with negative gradient, and that straightness is exactly what makes the motion simple harmonic.
Describing it in context is a four-mark pattern. Pendulum: the component of the weight along the arc, towards the lowest point. Floating object pushed down: upthrust now exceeds weight, so the net force is upward; pushed up, weight wins and the net force is downward.
F = −mω²x ties the force picture back to the kinematics: identify the constant in front of x and you have ω.
Prove it — watch it be true
- Read the SHM candidate on the a–x tester: straight line, through the origin, negative gradient — multiply the axis by m and that is the F–x graph the card demands
- Check the sign: for positive x the line sits below the axis, so F is directed back towards equilibrium, which is F = −kx = −mω²x
- Switch to the a ∝ sign(x) candidate: the force still points inward but is no longer proportional to x, so the F–x graph is no longer a line and the motion is not SHM