Free Mechanical Vibrations

  • Thread starter jrsweet
  • Start date
  • #1
32
0

Homework Statement


A mass m=4 is attached to both a spring, with spring constant k=37, and a dash-pot with damping constant c=4.

The ball is started in motion with initial position x0=1 and initial velocity v0=8 .
Determine the position function x(t).


Homework Equations





The Attempt at a Solution


So, the differential equation would be:
4x''+4x'+37x=0
4r^2+4r+37=0
r=-(1/2)+or- (1/2)sqrt(26)i

And so,
x(t)=e^(-.5t)(C1cos(.5sqrt(26)t)+C2sin(.5sqrt(26)t))
x'(t)=-.5e^(-.5t)(C1cos(.5sqrt(26)t)+C2sin(.5sqrt(26)t))+e^(-.5t)(-.5*C1sqrt(26)sin(.5sqrt(26)t)+.5*C2sqrt(26)cos(.5sqrt(26)t))

x(0)=C1=1
x'(0)=.5sqrt(26)C2-.5C1=8
=.5sqrt(26)C2=17/2
C2=17/sqrt(26)

And so,
x(t)=e^(-.5t)(cos(.5sqrt(26)t)+(17/sqrt(26))sin(.5sqrt(26)t))


Can anyone see anything wrong with this??
 

Answers and Replies

  • #2
tiny-tim
Science Advisor
Homework Helper
25,836
251
Hi jrsweet! :smile:

(have a square-root-: √ and try using the X2 tag just above the Reply box :wink:)

Where did your √26 come from? :confused:
 

Related Threads on Free Mechanical Vibrations

Replies
5
Views
4K
  • Last Post
Replies
3
Views
3K
  • Last Post
Replies
0
Views
2K
  • Last Post
Replies
3
Views
1K
  • Last Post
Replies
6
Views
3K
Replies
1
Views
1K
  • Last Post
Replies
7
Views
667
Replies
0
Views
1K
Replies
11
Views
288
Replies
6
Views
10K
Top