Explore BrainMass

# Differential Equations : Spring with Damping Force

Not what you're looking for? Search our solutions OR ask your own Custom question.

This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

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 ½ 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.

© BrainMass Inc. brainmass.com October 2, 2022, 12:16 pm ad1c9bdddf
https://brainmass.com/math/calculus-and-analysis/differential-equations-spring-damping-force-129435

#### 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 ½ 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.

\$2.49