By substituting zt and zt into both sides of the

Question

Question: Demonstrate that a complex exponential signal can also be a solution to the tuning-fork differential equation:

d²x = -kx(t)
dt²    m

By substituting z(t) and z*(t) into both sides of the differential equation, show that the equation is satisfied for all t by both of the signals

z(t) = X e^jω₀t  and  z*(t) = X* e^-jω₀t

Determine the value of ω0 for which the differential equation is satisfied.