Oscillations
Also known as: periodic motion, vibrations
Oscillations are repetitive back-and-forth movements about an equilibrium position, such as a swinging pendulum or a mass bouncing on a spring. They are described by amplitude, period, and frequency.
Any system pulled away from a stable equilibrium and pushed back toward it can oscillate. The amplitude is the maximum displacement from equilibrium, the period T is the time for one complete cycle, and the frequency f is the number of cycles per second, measured in hertz. The two are reciprocals, f = 1/T, and angular frequency ω = 2πf links them to the mathematics of rotation.
The most important special case is simple harmonic motion, which occurs when the restoring force is proportional to displacement and directed back toward equilibrium — the relationship F = −kx expressed by Hooke's law for a spring. Under that condition the displacement traces a sinusoid, x(t) = A cos(ωt + φ), and the motion is the projection of uniform circular motion onto a single axis.
Two standard systems produce the results worth memorising. A mass on a spring has period T = 2π√(m/k), so a heavier mass or a softer spring oscillates more slowly. A simple pendulum at small angles has period T = 2π√(L/g), which depends on length and gravitational field strength but not on the mass of the bob. In both cases the period is independent of amplitude, a distinctive property of simple harmonic motion.
Energy in an ideal oscillator is conserved and shuttles continuously between kinetic and potential form. Kinetic energy peaks at the equilibrium position where speed is greatest, potential energy peaks at maximum displacement where the system momentarily stops, and their sum stays constant. Real oscillators lose energy to friction and air resistance, so amplitude decays — this is damping. Driving a system near its natural frequency produces resonance, where the amplitude grows dramatically.
Mathematically, simple harmonic motion is the solution to the second-order differential equation m(d²x/dt²) + kx = 0, which is why the topic appears in engineering mathematics as well as physics.
AP Physics 1 devotes an entire unit to oscillations, testing the period formulas, energy analysis, and graphical interpretation of displacement, velocity, and acceleration over time. The FE Mechanical exam meets the same physics through ordinary differential equations in its mathematics section. And the CCNA borrows the vocabulary rather than the mechanics: wireless networking fundamentals describe radio signals by the frequency at which their electromagnetic fields oscillate, which is what 2.4 GHz and 5 GHz Wi-Fi bands refer to.
Key takeaways
- An oscillation is repetitive motion about an equilibrium position, described by amplitude, period, and frequency.
- Simple harmonic motion arises when the restoring force is proportional to displacement, as in F = −kx.
- A mass on a spring has period T = 2π√(m/k); a small-angle pendulum has period T = 2π√(L/g).
- Pendulum period does not depend on the mass of the bob, and neither system's period depends on amplitude.
- Energy alternates between kinetic and potential form; damping removes it and resonance amplifies the motion.