In: Physics
An object on a single oscillating string may be
modelled by differential equation x"(t)=-x(t)
x(t) is the signed length of the string at time t.
a) the trivial solution x(t) =0 satisfies the
differential equation. describe what physical scenario this
solution represents.
b) find at least three other solutions to the differential
equation
c) describe what it means for this differential equation to have
multiple solutions. what do the solutions represent.
d) suppose a string is damped by friction. propose and justify a
amendment to the differential equation that accounts for the
damping force.