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Vibration - Dynamics

  • Thread starter tommy100
  • Start date
  • #1
5
0

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[tex]\ddot{x}[/tex]+kx = F0sin[tex]\omega[/tex]t
Damped force vibration:
x = Asin([tex]\omega[/tex]t - [tex]\phi[/tex]) ,where [tex]\phi[/tex]=phase ans A=amplitude
NB [tex]\omega[/tex] 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[tex]\ddot{x}[/tex] coming off the side.

resolving forces:
[tex]\sum[/tex]Fx = m[tex]\ddot{x}[/tex] = -cx - kx + F

m[tex]\ddot{x}[/tex] + 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:

Answers and Replies

  • #2
674
2
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
5
0
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
 
  • #4
674
2
If this is a classical mechanics class, then I am sure your book has solved a very similar problem.
 

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