# Differential Equations : Spring with Damping Force

A body that weighs 16 lb. is attached to the end of a spring which is stretched 2 ft. by a force of 100 lb. It is set in motion from a position of Â½ foot from the equilibrium position of the spring with an initial velocity of -10 ft/sec. Assume the motion of this body is subject to a damping force that provides 6 lb of resistance to the motion for each foot per second of the body's velocity.

(a) Find the differential equation that governs the position of the body over time relative to the equilibrium position of the spring.

(b) Solve the differential equation.

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#### Solution Preview

A body that weighs 16 lb. is attached to the end of a spring which is stretched 2 ft. by a force of 100 lb. It is set in motion from a position of Â½ foot from the equilibrium position of the spring with an initial velocity of -10 ft/sec. Assume the motion of this body is subject to a damping force that provides 6 lb of resistance to the motion for each foot per second of the body's velocity.

(a) Find the differential equation that governs the position of the body over time relative to the equilibrium position of the spring.

First we need to find the spring constant

When the spring is ...

#### Solution Summary

Differential Equations and a Spring with a Damping Force are investigated. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.