An object on a single oscillating string may bemodelled 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 thedifferential equation. describe what physical scenario thissolution represents.
b) find at least three other solutions to the differentialequation
c) describe what it means for this differential equation to havemultiple solutions. what do the solutions represent.
d) suppose a string is damped by friction. propose and justify aamendment to the differential equation that accounts for thedamping force.
