← Physics — Std 12
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Oscillations

Ch. 5Std 12

Easy Overview

Think of a swing moving back and forth, or a guitar string vibrating after you pluck it. That repeated motion — to and fro, around a center point — is oscillation. This chapter is about why things keep moving back and forth, and how to describe that motion mathematically without losing your mind.

Simple Harmonic Motion (SHM)

SHM is the smoothest, most natural kind of oscillation. Imagine a mass on a spring. Pull it, let go — it bounces back and forth. The cool thing is the force bringing it back is proportional to how far you pulled it. More pull = more force back. That's Hooke's law. The motion follows a sine or cosine wave — smooth and predictable. The time for one complete back-and-forth is called the period, and it stays constant no matter how big the swing (for small swings, at least).

Parameters of SHM

Amplitude is how far the thing moves from center — the maximum displacement. Angular frequency (ω) is how fast it oscillates in radians per second. Phase tells you where in the cycle it starts. Think of a Ferris wheel — amplitude is the radius, frequency is how many rotations per second, and phase is whether you start at the top or bottom. All three together completely describe any SHM. The equation looks scary: x = A sin(ωt + φ), but it's really just describing a circle projected onto a line.

Energy in SHM

In SHM, energy keeps swapping forms. At the extremes (maximum displacement), all energy is stored as potential energy — like a stretched spring ready to snap back. At the center (equilibrium), it's all kinetic energy — maximum speed. The total energy stays constant (if there's no friction). It's like a playground swing — at the highest point, you're moving slow (mostly potential), at the bottom, you're fastest (mostly kinetic).

Simple Pendulum

A simple pendulum is just a weight hanging from a string. For small swings (less than about 15°), it behaves like SHM. The time period depends only on the length of the string and gravity — not on the mass of the bob or how big the swing is. That's why a heavier person and a lighter person on swings of the same length have the same time period. Longer string = slower swing. That's how pendulum clocks work — adjust the length to change the timing.

Key Points

  • •SHM happens when restoring force ∝ displacement (F = -kx).
  • •x = A sin(ωt + φ) is the general equation of SHM. A = amplitude, ω = angular frequency.
  • •Time period T = 2π/ω. Frequency f = 1/T.
  • •In SHM, energy keeps oscillating between kinetic and potential. Total energy = ½kA² (constant).
  • •Simple pendulum: T = 2π√(L/g). Period doesn't depend on mass.
  • •At equilibrium, velocity is maximum and acceleration is zero. At extremes, vice versa.

Practice Questions

  • Derive the expression for the time period of a simple pendulum.
  • A particle executes SHM with amplitude A. At what displacement from mean position is its kinetic energy equal to potential energy?
  • Show that the total energy of a body in SHM remains constant.
  • The length of a simple pendulum is increased by 4%. Find the percentage change in its time period.