# Determining the transfer function

grothem

## 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 $$\alpha$$
Rotational Damper, T=B $$\omega$$
Rotational Spring, T=K $$\theta$$

## The Attempt at a Solution

I'm having trouble relating the rotational forces to F.
F=m $$\ddot{x}$$

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

but basically, T = J $$\ddot{[tex]\theta$$}[/tex] + B$$\dot{[tex]\theta$$}[/tex] + K $$\theta$$
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?

#### Attachments

• controls problem.JPG
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Last edited:

viscousflow
You may want to consider making a free body diagram for each component. It should be seen that T=ma for starters.

CEL

## 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 $$\alpha$$
Rotational Damper, T=B $$\omega$$
Rotational Spring, T=K $$\theta$$

## The Attempt at a Solution

I'm having trouble relating the rotational forces to F.
F=m $$\ddot{x}$$

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

but basically, T = J $$\ddot{[tex]\theta$$}[/tex] + B$$\dot{[tex]\theta$$}[/tex] + K $$\theta$$
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?

T = J $$\ddot{\theta} + B\dot{\theta} + K\theta$$
$$\frac{\theta(s)}{T(s)}$$