The displacement–time graph traces a clean sine wave, and the energy bars show spring potential energy and kinetic energy constantly swapping while their total stays level (until damping is switched on). It is the same physics behind car suspension, a swinging pendulum, and a vibrating guitar string.
- What is the formula for the period of a mass on a spring?
- T = 2π√(m/k), where m is the mass in kilograms, k is the spring constant in newtons per metre, and T is the period in seconds. Doubling the mass makes the period longer by a factor of √2; doubling the spring constant makes it shorter by the same factor.
- Does amplitude affect the period of simple harmonic motion?
- No. In ideal SHM the period depends only on mass and spring constant, never on how far you stretch the spring before releasing it. Pull the mass down twice as far in this tool and time it: the period stays exactly the same.
- What is simple harmonic motion?
- Oscillation where the restoring force is directly proportional to displacement and always points back towards equilibrium (Hooke’s law, F = −kx). This produces a smooth sine-wave motion, seen in springs, pendulums at small angles, and many vibrating systems.
- What happens to the energy in an oscillating spring?
- It swaps continuously between spring potential energy (½kx², greatest at maximum stretch) and kinetic energy (½mv², greatest at equilibrium). With no friction or air resistance, the total stays constant; damping lets some leak away as heat each cycle.
- What are the units of the spring constant?
- Newtons per metre (N/m). A spring constant of 20 N/m means it takes 20 newtons of force to stretch or compress the spring by 1 metre.
- Where is simple harmonic motion seen in real life?
- Car suspension springs, a tuning fork, a swinging pendulum clock, a vibrating guitar string, and the quartz crystal inside a watch all rely on the same restoring-force physics modelled here.