Hooke's law is the straight line at the heart of every spring — and the doorway to oscillation. Hang a mass and watch the spring stretch by exactly x = mg/k, with the balanced weight and spring-force arrows drawn on it, because the force to stretch a spring is proportional to how far it stretches: F = k·x. Read the extension, force, stored energy ½kx² and period live; the F–x graph shows the line whose slope is k and whose shaded area is that energy. Then hit Release to oscillate to see simple harmonic motion, T = 2π√(m/k), and energy trading between elastic PE and kinetic KE. It all runs on your device.
You are in the Physics lab.
What the two vectors, the F–x line and the energy meter are telling you.
On the mass, the red arrow pointing down is its weight, W = m·g, and the blue arrow pointing up is the spring force, F = k·x. When the mass hangs still they are exactly equal and opposite — that balance is what fixes the extension at x = m·g/k, marked in centimetres on the ruler against the dashed natural length. Make the spring softer or the mass heavier and watch the stretch grow to keep the arrows matched.
The lower graph plots force against extension. Hooke's law makes it a straight line through the origin, and its slope is the spring constant k — a stiffer spring gives a steeper line. The green dot is your current operating point, and the shaded blue triangle beneath it is its area, ½·k·x², which is exactly the elastic potential energy stored in the spring. Because it is a triangle, doubling x quadruples the energy.
Press Release to oscillate and the mass bounces in simple harmonic motion about equilibrium with period T = 2π·√(m/k). The two-bar meter on the spring tracks the oscillation energy measured from equilibrium: at the top and bottom of each bounce it is all elastic PE, and as it flies through equilibrium it is all KE — but the two bars always add to the same total. That trade is what turns Hooke's law into a wave.
Proportional force, a stiffness constant, stored energy, and the leap to oscillation.
Stretch a spring and it pulls back with a force proportional to the extension: F = k·x. Pull twice as far and it resists twice as hard. The constant k — the spring constant — sets how stiff it is, in newtons per metre. Hooke's law holds until the spring is stretched past its elastic limit and stops springing back.
Hang a mass m and the downward weight is m·g. The spring stretches until its pull matches that weight, k·x = m·g, so the extension settles at x = m·g/k. A heavier mass or a softer spring gives more stretch; a stiffer spring gives less. Switching gravity between Earth, Moon and Jupiter changes m·g, so the same spring and mass rest at a different extension on each world.
Doing work to stretch the spring stores elastic potential energy E = ½·k·x² — the triangular area under the F–x line. It is the energy the spring gives back when it snaps home, and the reservoir that powers the bounce. Because of the x² it grows fast: stretch three times as far and you store nine times the energy.
Release the mass and the unbalanced spring force always points back toward equilibrium in proportion to the displacement — the exact recipe for simple harmonic motion. The mass oscillates with period T = 2π·√(m/k), independent of gravity: heavier is slower, stiffer is faster. Energy sloshes between elastic PE and kinetic KE while their sum stays fixed, which is why a mass on a spring keeps perfect time.
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Record force and the resulting extension; look for a proportional relationship.
Hooke’s law (F = kx) says spring force is proportional to extension, with k the stiffness read as the slope of force versus extension. Stored elastic energy is ½kx², valid until the spring passes its elastic limit.
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