Question

The normal modes of this system are products of trigonometric functions. (For linear systems, the time dependance of a normal mode is always sinusoidal, but the spatial dependence need not be.) Specifically, for this system a normal mode is described by
yi(x,t)=Ai sin(2p*x/?i)sin(2pfi*t)

Find the three lowest normal mode frequencies f1, f2, and f3.
Express the frequencies in terms of L, v, and any constants. List them in increasing order, separated by commas

Answer 1

Answer:

The normal modes of this system are products of trigonometric functions. (For linear systems, the time dependency of a normal mode is always sinusoidal, but the spatial dependence need not be.) Specifically, for this system a normal mode is described by

y(x,t)=A sin[2πx/λ] sin[(2πf)t]

Find the three lowest normal mode frequencies f1, f2, and f3.

Express the frequencies in terms of L, v, and any constants. List them in increasing order, separated by commas

In order of increasing frequencies we have $f_{1}, f_{2} , f_{3}$

$f_{1}= \frac{v}{2L} \\f_{2} = \frac{v}{L} \\f_{3} = \frac{3v}{2L}$

Explanation:

The attached images are  step by step calculation to the question, we are to obtain the fundamental frequency, the first overtone and second overtone;