Complete in Matlab:

a. Use the command dsolve to solve the differential equations below.

i. y + 3y = 0

ii. y + 3y = 0

iii. y + 3y = 0

iv. y + 3y = 0 v. y + 3y = 0

b. Graph each of the solutions in a. in the same window with 0 t 10.

c. Which of these equations does not represent a mechanical vibration? Why not? In your comments, explain how to recognize that the equation cannot describe a mechanical vibration i. from the graph of the solution, and also ii. from the coefficients of the original equation. (Recall how we have interpreted the coefficients m, b, and k where my + by + ky = 0.)

d. In your comments, classify the other four solutions as undamped, underdamped, critically damped, or overdamped.