## Equations of motion of a damped 2-dof system

## Equations of motion of a damped 2-dof system

(OP)

I am required to find the equations of motion for a damped free vibrating 2 dof system. The equations are needed for each mass individually depending on time i.e x1(t) and x2(t). I have found many examples of these equations with no damping but i can't seem to find any explanation for the damped free vibration case. The initial displacement may be varied but the initial velocity is always zero. Would anyone know the equations for each mass for the system? I have attached a diagram of the system

## RE: Equations of motion of a damped 2-dof system

## RE: Equations of motion of a damped 2-dof system

Cheers

Greg Locock

New here? Try reading these, they might help FAQ731-376: Eng-Tips.com Forum Policies http://eng-tips.com/market.cfm?

## RE: Equations of motion of a damped 2-dof system

This looks like an FEA 101 question, complete with the linear algebra. You need to write simultaneous equations for all your degrees of freedom.

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JHG

## RE: Equations of motion of a damped 2-dof system

However this is irrelevant, OP is stumbling over writing the equations in the first place. Work out the force in each spring as a function of the motion of its ends. Work out the acceleration of each mass as a function of the spring forces. Then substitute (c.D +k) for each spring value to get the force for the spring and damper combination. D is the differential operator d/dt, hence 1/D is integration.

There, I've done your homework for you.

Cheers

Greg Locock

New here? Try reading these, they might help FAQ731-376: Eng-Tips.com Forum Policies http://eng-tips.com/market.cfm?

## RE: Equations of motion of a damped 2-dof system

If you want more precise enunciation of the method, you can download the spreadsheet I developed from my website (http://rmniall.com), then trace the input data through to the development of the required equations.