Home / Topics / Work, Energy & Power
Energy in spring-mass systems
Intermediate
Total energy ½kA² is shared between kinetic and spring potential.
E = ½kA²The total energy E = ½kA² is constant. At displacement x the kinetic energy is ½k(A² − x²), and speed is max at x = 0.
k = 50 N/m, A = 0.2 m: E = 1 J.
Speed depends on amplitude and position, not gravity (for a horizontal system).
In more detail
A mass on a spring oscillates as energy swaps between spring potential and kinetic energy. The total energy is one half k A squared, where A is the amplitude.
Real-world uses
- Car suspension springs absorb and return energy when driving over bumps.
- Mechanical watches use balance springs that store and release energy.
- A car's suspension spring oscillates after a bump, and its total energy ½kA² stays nearly constant apart from damping losses.
Open the interactive lesson, with simulation and quiz →
Frequently asked questions
Where is the speed maximum?
At the equilibrium position, where the spring force is zero and the kinetic energy is greatest.
What affects the total energy?
Only the spring constant and the amplitude, not the mass.
What is the amplitude A in this formula?
The maximum displacement from equilibrium, which is where the spring holds all the energy as potential energy.
Related topics in Work, Energy & Power
Conservation of mechanical energy · Energy conservation in free fall · Energy on a pendulum · Roller coaster and loops · Energy loss to friction · General energy conservation