A particle A , of mass 1 kg, moves along a frictionless horizontal track. The pa

Question

A particle A, of mass 1 kg, moves along a frictionless horizontal track. The particle is attached to a fixed point O by a model damper, and to another point B by a model spring as shown in the diagram. The two points O and B are a distance 2 metres apart on the track. The damping constant is 15.49 Ns m-1. The spring has stiffness 20.31 Nm-1 and natural length 1.047 metre. The displacement of the particle, x, is measured from O.

A particle A, of mass 1 kg, moves along a frictionless horizontal track. The particle is attached to a fixed point oby a model damper, and to another point B by a model spring as shown in the diagram. The two points 0 and B are a distance 2 metres apart on the track. The damping constant is 15.49 Ns m'. The spring has stiffness 20.31 Nm and natural length 1.047 metre. The displacement of the particle, x, is measured from 0. Calculate the equilibrium position of the particle, measured from 0, giving your answer to 3 decimal places. oDOwn, n = 1

Explanation / Answer

Under equilibrium the spring will not have any stored energy. Because If any energy is left it will be consumed by the damper.Hence the spring will attain it's natural length which is 1.047 Ns m-1.Hence answer is 2-1.047=0.953 m from point O.

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