Question 2 A beehive hangs from a branch of a tree. The tree branch is ex ible, and behaves like a spring. The system can be modelled as a mass suspended from a spring. The mass of the beehive is 30kg. The branch acts as a spring with spring constant k 2 720 N ml. Air resistance applies a damping force with damping constant B = 300 N s m'l. Assume the beehive moves only vertically (ie, ignore any horizontal movement). Let y(t) be the position of the beehive in metres below its equilibrium position, at time t seconds. The equation of motion of the system is 303;" + 300y' + 7203; = 0 (t > 0) (a) Find the general solution of the ODE. (b) A hungry bear grabs the beehive, pulls it down 0.5m from its equilibrium position, and releases the beehive from rest. Solve for y(t), and sketch the graph of y(t) vs. :3