# Vibration - Dynamics

1. May 7, 2009

### tommy100

1. The problem statement, all variables and given/known data
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]

2. Relevant 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

3. 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

Last edited by a moderator: May 4, 2017
2. May 7, 2009

### 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.

3. May 7, 2009

### tommy100

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

4. May 7, 2009

### nickjer

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