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Determining the transfer function

  • Thread starter grothem
  • Start date
  • #1
23
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Homework Statement


Determine the transfer function between output x and input F for the following mass-spring system. (see attached image)


Homework Equations


F=ma
Inertia, T = J [tex]\alpha[/tex]
Rotational Damper, T=B [tex]\omega[/tex]
Rotational Spring, T=K [tex]\theta[/tex]

The Attempt at a Solution


I'm having trouble relating the rotational forces to F.
F=m [tex]\ddot{x}[/tex]

k so I guess the latex equations aren't coming out right.

but basically, T = J [tex]\ddot{[tex]\theta[/tex]}[/tex] + B[tex]\dot{[tex]\theta[/tex]}[/tex] + K [tex]\theta[/tex]
The sum of all forces, including inertial forces must equal zero, and I need to convert to the laplace domain to get X(s)/F(s), but how does T fit into that?
 

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Answers and Replies

  • #2
272
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You may want to consider making a free body diagram for each component. It should be seen that T=ma for starters.
 
  • #3
CEL
656
0

Homework Statement


Determine the transfer function between output x and input F for the following mass-spring system. (see attached image)


Homework Equations


F=ma
Inertia, T = J [tex]\alpha[/tex]
Rotational Damper, T=B [tex]\omega[/tex]
Rotational Spring, T=K [tex]\theta[/tex]

The Attempt at a Solution


I'm having trouble relating the rotational forces to F.
F=m [tex]\ddot{x}[/tex]

k so I guess the latex equations aren't coming out right.

but basically, T = J [tex]\ddot{[tex]\theta[/tex]}[/tex] + B[tex]\dot{[tex]\theta[/tex]}[/tex] + K [tex]\theta[/tex]
The sum of all forces, including inertial forces must equal zero, and I need to convert to the laplace domain to get X(s)/F(s), but how does T fit into that?
You have already your differential equation:

T = J [tex]\ddot{\theta} + B\dot{\theta} + K\theta[/tex]

Now apply the Laplace transform to obtain the transfer function in rotational variables:

[tex]\frac{\theta(s)}{T(s)}[/tex]
 

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