Continuous Systems

Prof. TVK Bhanuprakash

Transverse Vibration of a String or Cable

wave equation

Boundary Conditions

Solution using Method of Separation of variables

Free Vibration of a String with Both Ends Fixed

This equation gives all possible vibrations of the string; the particular vibration that occurs is uniquely determined by the specified initial conditions. The initial conditions give unique values of the constants Cn and Dn . If the initial conditions are specified as

Longitudinal Vibration of a Bar or Rod

Orthogonality of Normal Functions

This equals zero for any combination of BCs

orthogonality principle for the normal functions

Lateral Vibration of Beams

Solution

The cord of a musical instrument is fixed at both ends and has a length 1.5 m, diameter 0.4 mm, and density 7000 kg/m3. Find the tension required in order to have a fundamental frequency of (a) 1 Hz and (b) 5 Hz.