Given the following homogeneous ODE 2y 12y 68y 0 with ini

Given the following homogeneous ODE 2y + 12y + 68y = 0 with initial conditions y(0) = 3. y(0) = 0 Does the homogeneous response exhibit oscillations? Estimate the time to reach steady state. Describe the nature of the homogeneous response (a sketch may help).

Solution

A) yes from the given equation homogenous response exhibit oscillation

B) time = 32 seconds

C) nature = steady