# Differential equation and a spring

I am looking for a detailed solution. I need set up, solving, and final result. Therefore, I need solution of the second order DFQ. Finally for the description of the movement as time goes to infinity, I need what type of motion is that.

a. An 8lb weight is attached to a spring suspended from the ceiling. When the weight comes to rest at equilibrium, the spring has been...

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#### Solution Preview

See the attached file.

(a) First we should find the spring constant k = F/x = 8/4 = 2 lb/in ....(1)

c = 40 lb-s/ft = 40 lb-s/12 in = 3.333 lb-s/in

When the mass is displaced x(t) from this position the spring is stretched an amount x(t). Thus there are equal and opposite forces (F) at the ends of the spring. The force F is given by F = kx(t). ...

#### Solution Summary

This is a question involving differential equations to find motion of the weight of a spring.