Question: ( b ) Consider the general solution to equation ( 1 ) with the boundary conditions ( 2 ) , i . e . for

(

)

Consider the general solution to equation

(1)

with the boundary conditions

(2),

.

.

for general initial conditions. Note that the amplitudes of all the normal modes will decay exponentially over time. Most of these amplitudes will oscillate as they decay because they include sine or cosine terms. How many amplitudes do NOT oscillate?

( b ) Consider the general solution to equation (

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