Hooke’s Law
Drag the mass to stretch or compress the spring, then release and watch it oscillate. The force is proportional to displacement: F = −kx. Add multiple springs to compare different stiffness values side by side.
T = 2π√(m/k)
About this lab
Hooke’s law, published by Robert Hooke in 1678 (as an anagram in 1676), states that the force exerted by a spring is proportional to its displacement from equilibrium: F = −kx, where k is the spring constant and x is the displacement. The negative sign indicates the force always acts to restore the system to equilibrium.
When a mass m is attached to a Hookean spring and released from displacement, it undergoes simple harmonic motion with period T = 2π√(m/k). The motion is sinusoidal: x(t) = A·cos(ωt + φ), where ω = √(k/m) is the angular frequency. The velocity is 90 degrees out of phase with displacement, and the force-displacement relationship is a straight line through the origin with slope −k.
With damping (a force proportional to velocity, F = −bv), the oscillations decay exponentially. The system is underdamped when b < 2√(mk), critically damped when b = 2√(mk), and overdamped when b > 2√(mk). In the underdamped case, the amplitude envelope decays as e^(−bt/2m) while the frequency decreases slightly.
Energy oscillates between kinetic energy (KE = ½mv²) and potential energy (PE = ½kx²). Without damping, the total energy is conserved. The energy bars above show this exchange in real time — when one is at maximum, the other is at zero.