3.1 and 3.3)
First, let us check if the given function satisfies the boundary condition.
The boundary conditions are no displacement at the boundaries.
thus checking for x = 0,
similarly for y=0,
for x = a,
for y = b
thus the given satisfies the boundary condition.
now to check if it satisfies the wave equation:
and
thus satisfies the wave equation if
3.5) for this,
now and
thus (n,m) and (m/2,2n) are a pair of modes which have the same frequency.
. (40 points: A membrane is stretched under tension r with uniform surface density o. (Small-amplitude)...