Amass of 0.5kg is attached to a spring (spring constant 8 n/m) suspended from the ceiling an external downward force of f(t)-50 cos(wt) n acts on the mass, where ω-0. assume that the acceleration due to gravity is 9.8m/s', and the damping force is 1 times the velocity of the mass, where β-0. the mass is set into motion from the equilibrium position with an initial downward velocity of 2 m/s. let y(t) be the displacement of the spring (in metres) below the equilibrium position at time t seconds. (a) using newton's law, show that the equation of motion for the spring-mass system is include a diagram of all the forces acting on the mass. (b) for which values of b will there be weak damping? give a rough sketch of the homogeneous solution in this case. (you do not need to solve the differential equation.) (c) suppose b-0 (i) what value of the driving frequency w will cause resonance? (ii) for the case of resonance, find the position of the mass at any time.