The suspension of a modified baby bouncer is modelled by a model spring AP with stiffness k₁ and a model damper BP with damping coefficient r. The seat is tethered to the ground, and this tether is modelled by a second model spring PC with stiffness k₂. Model the combination of baby and seat as a particle of mass m at a point P that is a distance r above floor level. The bouncer is suspended from a fixed support at a height h above the floor. The suspending spring has natural length 11, while the tethering spring has natural length l₂. Take the origin at floor level, with the unit vector i pointing upwards, as shown in the following diagram. ki, 1 h P AB -000000 k2, 2 000000 (a) Draw a force diagram showing all forces acting on the particle P. (b) Copy and complete the following table, and hence write down the force on particle P due to each model spring. The notation is the same as that used in the unit. Spring Spring Natural Extension Stiffness H length length AP 11 CP 12 k1 k₂ (c) Copy and complete the following table, and hence write down the force on particle P due to the model damper. The notation is the same as that used in the unit. Damper Rate of change Damping R length of length constant r (d) Model the remaining forces acting on the particle P, and hence show that the equation of motion of the mass is mi+ri+ (k₁+k2)x = k₁(h-l₁) + k2l2-mg. (e) In SI units, suppose that m = 10, k₁ = 150, k₂ = 100, r = 20, h = 1.5, ₁ = 0.5 and 12 = 0.25. Determine the natural angular frequency of the system to two decimal places. Using the same data, calculate the damping ratio for this mechanical system to two decimal places, and hence state whether the system undergoes strong, weak or critical damping. Comment on whether this damping is appropriate for a baby bouncer.