(a) State the following ODE properties: independent variable, dependent variable, order, linear-

ity and homogeneity.

(b) Derive the characteristic equation for this ODE and find the corresponding roots of the ODE.

Note the trial solution used and simplify your answer using w = √K/M. Briefly describe the

expected physical behaviour of this system, based on the roots of the characteristic equation.

(c) Consider that the system has an object with m = 2 kg, a spring with spring constant k = 50

N m¹ and a natural length of 1 m. If the spring is stretched to a length of 2 m (i.e. beyond

its natural length) and released with an initial velocity of 0m s¹, find the particular solution

to the ODE.