Question

This problem is an example of over-damped harmonic motion.
A mass m=4kg is attached to both a spring with spring constant k=72N/m and a dash-pot with damping constant c=36N⋅s/m

The ball is started in motion with initial position x0=−3m and initial velocity v0=4m/s

Determine the position function x(t) in meters.

Answer 1

DE is given by

here

m=4

c=36

k=72

find roots

for 2 real roots, general solution is

.....................(1)

.

here we have y(0)=-3

................put it back in equation 1

....................(2)

.

take derivative

here we have y'(0)=4

.................put it back in equation 2

.

.

position function is