Oscillations — Class 11 Physics

A motion that repeats itself at regular intervals is periodic, and a to-and-fro motion about a mean position is oscillatory; every oscillation is periodic though not every periodic motion is oscillatory. The period is the time for one cycle and the frequency is measured in hertz. The simplest oscillation is simple harmonic motion (SHM), in which the displacement varies sinusoidally as , where is the amplitude, the angular frequency and the phase constant. SHM is the projection of uniform circular motion on a diameter. Velocity and acceleration are derived; acceleration is always directed toward the mean position and proportional to displacement. The force law defines a linear harmonic oscillator with . The kinetic and potential energies vary with time but their sum, the total energy , is constant. A simple pendulum executes SHM for small angles with period , independent of mass and amplitude. These ideas underlie springs, pendulums and the vibrations of strings and air columns, and they form the basis for studying damped and forced oscillations and resonance.