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Question: how would the force diagram look like and stage by...

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Question 5 (Unit 10) 16 marks The suspension of a modified baby bouncer is modelled by a model spring AP with stiffness ki 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. e bouncer is suspended from a fixed support at a height h above the floor. The suspending spring has natural length l1, while the tethering spring has natural length (2. Take the origin at floor level, with the unit vector i pointing upwards, as shown in the following diagram. A B k1,11 62, 12

(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 12) on particle P due to each model spring. The notation is the same as that used in the unit. Spring Spring Natural Extension StffcssH length length 12] (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 S lengthof 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 (e) In SI units, suppose that m = 8, k-130, k2 = 70, r h 0.75 and 12 0.75. 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 40, h= 2,

How would the force diagram look like, and stage by stage calculations?

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