A mass on the end of a spring never simply returns to rest — it overshoots, is pulled back, and does it all again. This diagram shows the restoring force behind that steady back-and-forth, and the sine wave the motion traces in time.
Take a block on a smooth, frictionless table and tie it to a spring fixed to a wall. Pull the block to one side and let go. It does not creep back and stop — it sweeps through the centre, stretches the spring the other way, and comes back again. This steady, repeating to-and-fro is simple harmonic motion, and it is one of the most common patterns in physics.
Two things are in a tug of war. The spring provides a restoring force that always points back toward the equilibrium position and grows with the displacement, F = −k x. The mass supplies inertia: once it is moving it keeps going. The spring makes it turn around; the mass makes it overshoot. Together they produce the oscillation.
Because the restoring force is proportional to the displacement, the acceleration is too — and that special relationship gives motion that repeats exactly, with position tracing a smooth sine wave against time. The time for one full cycle is the period T, and every swing takes the same time.
Stretch the spring to one side and let go. The displacement from equilibrium is what starts everything: the further you stretch it, the larger the forces that follow.
The spring exerts a restoring force toward equilibrium, proportional to the displacement: F = −k x. The minus sign means the force always points opposite to the way the mass has been moved.
The mass picks up speed and races through equilibrium, where the spring's force is momentarily zero. Because nothing slows it there, it carries on past the centre and stretches the spring the other way.
Elastic energy stored in the spring becomes kinetic energy of the moving mass and back again. At each extreme it is all spring energy; as the mass passes the centre it is all motion. Neither is used up — the two simply trade places.
Overshoot, pull back, overshoot — the motion settles into a steady back-and-forth. Plotted against time the position traces a smooth sine wave, and the time for one full cycle is the period T, the same for every swing.
It is a back-and-forth motion in which the restoring force is proportional to the displacement and always points back toward equilibrium. The position then traces a smooth sine wave, like the mass on a spring shown here.
Because it has already picked up speed by the time it reaches equilibrium. The spring's force is zero there, so nothing slows it, and it carries on past the centre until the spring pulls it back.
Because the spring obeys Hooke's law: its pull is proportional to how far it is stretched or compressed. That proportional restoring force is exactly the condition for simple harmonic motion.
No. For an ideal spring the period depends only on the mass and the spring stiffness, not on the amplitude — a small swing takes the same time as a large one.
It swaps between elastic energy stored in the spring and kinetic energy of the moving mass. At each extreme it is all spring energy; as the mass passes through equilibrium it is all motion.