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The suspension of a modified baby bouncer is modelled by a model spring AP with stiffness, and a model damper BP with damping coefficient The seat is tethered to the ground, and this tether is modeled by a wond model spring PC with stiffness Model the combination of baby and as a particle om at a point that is a distance above floor level The bouncer is suspended from a fixed support at a heighth above the floor The spending spring natural ngth while the tethering sprinhas natural leagth . The the originat for level with the unit vector i 2004 (a) Draw a force dingram 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 that and in the unit. Spring Spring length Natural Extension length Stiffness АР CPI (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 Dumper Rate of change Damping length of length constant (d) Model the r that the g aining for acting on the particle P. and hence show ood took the mass is I sa-mg. (e) in Slits, we thatm-2. 90 1 62 -0.75 and 1-0.75. Determine the natural gar 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 state whether the system undergoes , weak or critical damping Comment on whether this damping is appropriate for a baby bouncer.
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