Mechanics Vibrations Homework: Piston Displacement & Time Calculation

[tom l]

Homework Statement

A piston of mass 4.53(kg) is traveling in a tube with a velocity of 15.24(m/s). It engages a spring of stiffness 350 (N/cm) and a damper with a coefficient of 1.75 (N.s/cm)

What is the maximum displacement of the piston and how long does it take to reach this point?

Homework Equations

F= -kx
where
x is the displacement vector - the distance and direction in which the spring is deformed
F is the resulting force vector - the magnitude and direction of the restoring force the spring exerts
k is the spring constant or force constant of the spring.

velocity=displacement/time

Damping : http://en.wikipedia.org/wiki/Damping

The Attempt at a Solution

I have the solutions, Max. Displacement = 128.6(mm), Time Taken = 0.0157(s). I am stuggling to find a link between the known data and the displacement. Hope you can help

 

[rpf_rr]

Integrate the wikipedia equation with the conditions x(0)=0, v(0)=15.24 (cauchy problem); the system is underdamped, you will find a solution like exponential*sin, for the maximum displacement set the condition v(t)=0, i found it at t=0.01572s, if you want further help i can give you the analytic solution but I'm not good at Latex, it's more like a math exercise than a physic's one