A mass is released from rest at the amplitude of a spring. Displacement, and in GCSE mode velocity and acceleration, are plotted as it moves. Angular frequency is ω = √(k/m). The sliders stay in the underdamped region, so the mass keeps oscillating while light damping makes the amplitude fall.
Simple harmonic motion means the acceleration is proportional to the displacement from equilibrium and directed back toward it: a = −ω²x. The minus sign is the restoring part. For this spring, Hooke’s law gives that condition with ω = √(k/m).
With no damping, T = 2π/ω = 2π√(m/k). Period depends on mass and spring stiffness, not on amplitude, as long as the spring obeys Hooke’s law. The simulation is released from rest, so the first moment is all displacement and no velocity.
At maximum displacement, velocity is zero and acceleration has its greatest size. At the equilibrium position, acceleration is zero and speed is greatest. Velocity is the gradient of the displacement–time graph; acceleration is the gradient of the velocity–time graph.
With no damping, energy swaps between elastic potential ½kx² and kinetic ½mv², and the total stays constant. Damping removes mechanical energy, so the amplitude falls. Light damping gives an approximately exponential envelope. The period becomes 2π/ωd, with ωd a little less than ω, so the period is a little longer.
GCSE meets oscillations through waves and pendulums in a qualitative way. The defining equation, the mass–spring period and damping are A level and IB. There is no driving force here, so the page does not show resonance.
The spring and the support are massless, and the mass is released from rest. External driving is ignored. Very heavy damping that stops the motion before a full cycle is outside the slider range: every allowed setting still oscillates.