EJC Physics H210 Oscillations 2023 1. Notes (2023)_FULL For Microsite

Swings are one of a child’s earliest interactions with free oscillations and resonance. Find out why the frequency of oscillations does not differ with the mass of the person on it, and how our parents, siblings and friends naturally supply extra bursts of energy into the swing system under resonant conditions. Content • Simple harmonic motion • Energy in simple harmonic motion • Damped and forced oscillations, resonance Learning Outcomes Candidates should be able to: (a) describe simple examples of free oscillations (b) investigate the motion of an oscillator using experimental and graphical methods (c) show an understanding of and use the terms amplitude, period, frequency, angular frequency and phase difference and express the period in terms of both frequency and angular frequency (d) recall and use the equation 2ax =− as the defining equation of simple harmonic motion (e) recognise and use 0 sinx x t = as a solution to the equation 2ax =− (f) recognise and use the equations 0 cosv v t = and 22 0v x x=  − (g) describe, with graphical illustrations, the changes in displacement, velocity and acceleration during simple harmonic motion (h) describe the interchange between kinetic and potential energy during simple harmonic motion (i) describe practical examples of damped oscillations with particular reference to the effects of the degree of damping and to the importance of critical damping in applications such as a car suspension system (j) describe practical examples of forced oscillations and resonance (k) describe graphically how the amplitude of a forced oscillation changes with driving frequency near to the natural frequency of the system, and understand qualitatively the factors which determine the frequency response and sharpness of the resonance (l) show an appreciation that there are some circumstances in which resonance is useful, and other circumstances in which resonance should be avoided We have studied the kinematics of bodies in (i) straight line, (ii) projectile and (iii) circular motions. Oscillatory motions are another type of motion that can be often seen in everyday life: the swinging pendulum of a grandfather clock, the vibrations of a bus, and the waves on the strings of a guitar. Other non-visible examples include the electro-magnetic oscillations emitted by wireless equipment, gaseous atoms and molecules that propagate sound waves, and the lattice vibrations of atoms. To better understand how these systems work, it is important we learn the mechanics of oscillations.

If an oscillation repeats over time, it is a periodic motion. An oscillation begins when a system is perturbed from a condition of stable equilibrium. Force(s) tend to arise as a result of the initial disturbance, to bring the system back to the state of stable equilibrium – these are generally known as restoring forces. The initial perturbation introduces an amount