# Vibration - Dynamics

## Homework Statement

Determine the max and min values of x and their times from 0 to 2s
initial conditions X0 = 0, V0 = 1m/s
http://img266.imageshack.us/img266/2198/figure1.jpg [Broken]

## Homework Equations

Undamped force vibration:
m$$\ddot{x}$$+kx = F0sin$$\omega$$t
Damped force vibration:
x = Asin($$\omega$$t - $$\phi$$) ,where $$\phi$$=phase ans A=amplitude
NB $$\omega$$ should not be superscripted

## The Attempt at a Solution

ive drawn a free body diagram as follows
http://img266.imageshack.us/img266/5150/freebody.jpg [Broken]
forget to add m$$\ddot{x}$$ coming off the side.

resolving forces:
$$\sum$$Fx = m$$\ddot{x}$$ = -cx - kx + F

m$$\ddot{x}$$ + cx + kx = F

Not sure where to go from here, ultimately i need to plot a graph to show the response of the 10kg mass and see where the max and min distances (x) happen and at what times

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The damping force is proportional to the velocity and not displacement. Then you would solve the 2 homogenous solutions and the steady state solution. You can find how to solve the ODE or the actual solutions on many websites.