Differential Equations 6

MAT 275 Activity 6 (12 points)

Mass Spring System

NAME____________________________ Date: ___________

(2 pts extra credit)

A mass that weighs 8 lb stretches a spring 4 in. The mass is attached to a dashpot mechanism that

has a damping constant of 0.25 lb-sec/ft. The system is acted on by an external force of t8sin6 lb. The mass is pulled down 3 in. and then released.

a) [2 pts] Determine the spring constant.

b) [4 pts] Write the differential equation governing the motion of the mass. Also write the initial conditions.

c) [4 pts] Determine the transient motion of the damped mass-spring system.

d) [4 pts] Determine the steady periodic oscillations of the damped mass-spring system.