Consider ? + c? +y = 0, and assume y(0) = 1, ÿ(0) = 0.(a) Why is this a homogeneous system?
(b) What would change if this was to be an inhomogeneous system?When is this inhomogeneous aspect applied - this is a technicalpoint, but helps us to understand that the initial condition is anexternal input too, but is *only* applied at t = 0?
(c) Choose e to make this problem overdamped/criticallydamped/underdamped.
(d) Follow the 3-step procedure to solve this homogeneous systemfor the ho- Imogeneous solution y which we call y: Step 1: Get yh.Step 2: Satisfy condition, and Step 3: Sketch. • Solve theoverdamped case where c is the critically damped version where c isincreased by 1 past the critically damped value. Solve thecritically damped case, • Solve the underdamped case where e is thecritically damped version where c is reduced by 1 below thecritically damped value.
