CBSE Class 11 — Notes, Chapters & Practice Quizzes

Chapter 6: Oscillations

Summary

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 \(T\) is the time for one cycle and the frequency \(\nu=1/T\) is measured in hertz. The simplest oscillation is simple harmonic motion (SHM), in which the displacement varies sinusoidally as \(x(t)=A\cos(\omega t+\phi)\), where \(A\) is the amplitude, \(\omega\) the angular frequency and \(\phi\) the phase constant. SHM is the projection of uniform circular motion on a diameter. Velocity \(v=-\omega A\sin(\omega t+\phi)\) and acceleration \(a=-\omega^{2}x\) are derived; acceleration is always directed toward the mean position and proportional to displacement. The force law \(F=-kx\) defines a linear harmonic oscillator with \(\omega=\sqrt{k/m}\). The kinetic and potential energies vary with time but their sum, the total energy \(E=\tfrac12 kA^{2}\), is constant. A simple pendulum executes SHM for small angles with period \(T=2\pi\sqrt{L/g}\), 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.

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