# Free vibrations question

I know this question has already been asked, but the given answer di not help me. Hopefully someone can post their full solution?

A piston of mass 4.53(kg) is travelling 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

## Answers and Replies

NascentOxygen
Staff Emeritus
Science Advisor
Hi Lukergr. http://img96.imageshack.us/img96/5725/red5e5etimes5e5e45e5e25.gif [Broken]

The damper resists with a force proportional to velocity, with units N per m/s, written F=-k.x' so it's a 2nd order differential equation you'll be looking to solve. Motion of the piston is resisted by both the spring and the damper. You'll find a worked example in almost every textbook on physics or calculus 101.

Last edited by a moderator:
BiGyElLoWhAt
Gold Member
Is this a diff eq based course?