The solution should be your work. DO NOT USE someone else's work. Please show all steps in detail.

Consider the differential equation m\"(t} = 10sin($(t}} t). It can be interpreted as the equation of motion for a pendulum with an attached spring. {a} Rewrite this second order ODE as a system of two rst order ODEs. {b} Find the differential equation % = f{m,y) for the trajectories of the system from part {a}I and solve it. {c} Plot the trajectories for initial conditions: i. 32(0) = 211', $10) = II]. ii. mm) = 311', 3'03) = I]. {d} Find numericallyF the equilibrium points. {e} Determine the stabilitj.F of the equilibrium points based on the shapes of trajectories