Question 2 A beehive hangs from a branch of a tree. The tree branch is flex- 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 = 720 N m'l. Air resistance applies a damping force with damping constant ,6 = 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;\" + 3003/ + 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. t. (c) Suppose instead that the bear climbs on to the beehive and stays attached to the beehive as it moves. The bear's mass is also 30kg so the total mass of beehive and bear is 60kg. Air resistance is unchanged. Again the beehive is released from rest 0.5m below its equilibrium position. Draw a graph of y(t) in this case and briey explain your reasoning. Hint: you do not need to solve for y(t)