Math Problem Solver

A thin metal rod is struck with a hammer and vibrates, with the amplitude of the vibration decaying over time. The displacement, s(x,t)

, of the rod from equilibrium at point x

and at time t

is described by the following function:

s(x,t)=Acos(kx−wt)e−mt

where k

, w

, and m

are constants representing the wavenumber, angular frequency, and decay rate respectively.

a) By taking the partial derivative of s(x,t)

with respect to t

, find an expression for the velocity of the vibrating rod, v(x,t)

.