A String of length L has one of its extremities fixed and the other one loose.
A. What's the equation for the normal mode frequencies?
B. Draw a snapshot of the string for the 1st 3 normal modes
The Attempt at a Solution
My idea was to follow the same line of thinking for a string with both extremities fixed. Then we can assume that
y(x, t) = g(x).cos(wt + d) --(1)
and (1) must be solution of the wave equation, and after some math we get the general solution
A(x)'' + A.k^2 = 0, k = w/v --(2)
we know that A(0) = 0, since the x=0 extremity is fixed and the general solution for 2 is
A(x) = b.cos(kx) + c.sin(kx)
so, b = 0 and A(x) = c.sin(kx)
since A(x) != 0, we know that c != 0, but there's no other known condition in order to compute possible values for k
any ideas? and.. tbh i dunno if i can assume everything i did since 1 of the extremities is loose. help pls! :D