1.1 Introduction
1.1 Oscillations or Vibrations
1.1 Oscillations or Vibrations some important points
1.1 Wave Quantities
1.1 Wave Properties
1.1 Wave Types
1.1 Speed of Waves
1.1 Simple Harmonic Motion
1.1 Derivation of Period and Frequency for SHM
1.1 Energy in Simple Harmonic Motion
1.1 SHM & Simple Pendulum
1.1 Reflection and Transmission
1.1 Summary
Unit 1.1 Multiple Choice Questions - Waves
Unit 1.1 Multiple Choice Answers - Waves

 

Unit 1.1 Simple Harmonic Motion (SHM)

Many of the disturbances we have considered so far have been sudden and short-lived, set up by a brief motion like snapping one end of a rope. In each case, you see a single wave running along the medium with a certain speed. Recall, this kind of wave is called a pulse.

— Now we consider periodic waves – regular continuous rhythmic disturbances in a medium, resulting from periodic vibrations of a source.

— One of the best examples is the periodic vibration is a swinging pendulum.

— Neglecting the effects of air resistance, the pendulum swings are virtually identical as the swing repeats itself over and over again in time.

Another system to show SHM.

— If the left end of a taut rope is fastened to the oscillating (vibrating) weight on a spring as the weight vibrates up and down a wave propagates along the rope.

— The wave takes the form of a series of moving crests and troughs along the length of the rope.

— The source executes “simple harmonic motion” up and down. Every point along the length of the rope executes simple harmonic motion in turn.

shm1

— This diagram illustrates a periodic wave moving to the right with snapshots taken every one-quarter period.

— We follow the progress of the crest that started out from the extreme left at time t = 0.

— The time it takes this crest to move a distance of one wavelength is equal to the time required for one complete oscillation of the source during one period of oscillation T.

shm2

shm2

These are two examples of how movement in one plane can produce simple harmonic motion from three dimensional movement.

Above the particle moves in a circular motion with constant speed and the linear projection of its x displacement is SHM.

Simple harmonic motion can be defined as oscillatory movement where the restoring force is proportional to the displacement from an equilibrium position.

Fr = -kx

In the animation below the displacement vs time graph is drawn on the right of the oscillating spring mass sytem. It traces the motion for two oscillations.

Note the practical meaning of period (time for one complete oscillation) amd amplitude (maximum displacement) are illustrated.

shm spring

Exercise 1.1.9:

(a) try to identify other points on the graph which can be used to measure period.

(b) another displacement which could be labelled amplitude.

 

Concept by Kishore Lal. Programmed by Kishore Lal... Copyright © 2015 Kishore Lal. All rights reserved.