How Do You Find Max and Min Values of Oscillating Motion in Dynamics?

[tommy100]

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

Homework Equations

Undamped force vibration:
m\ddot{x}+kx = F₀sin\omegat
Damped force vibration:
x = Asin(\omegat - \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
forget to add m\ddot{x} coming off the side.

resolving forces:
\sumF_x = 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

 

[nickjer]

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.

 

[tommy100]

Many thanks for your reply
Could you post a link or 2 to help me with this problem please
hope this doesn't go against forum rules
Regards
Tommy100

 

[nickjer]

If this is a classical mechanics class, then I am sure your book has solved a very similar problem.