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Springer

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## Homework Statement

Give governing equations for the system about its static equilibrium, assuming small vibrations

System consists of two springs located under 45 degrees to the vertical (both have same k-value) in undisturbed situation. Lower ends of the springs are attached to each other and to massless rod with length D, upper ends to immovable supports. The massless rod has point mass (m) at the lower end. System can move vertically and horizontally and is exposed to gravity.

## Homework Equations

Displacement method: mx"+cx'+kx = F(t)

## The Attempt at a Solution

System has 3 degrees of freedom (horizontal (x2) , vertical (x1) and rotation of pendulum around supension (theta))

I suggested:

mx"1 = -1/2*(k*sqrt(2)*x1) - 1/2*(k*sqrt(2)*x1) + mg

mx"2 = -1/2*(k*sqrt(2)*x2) + 1/2*(k*sqrt(2)*x2)

J(theta)" = -m*g*D*(theta)

The last equation under the assumption of small angles of the massless rod.

However, in this case it results in a decoupled dynamic system which I suppose is incorrect?

Thanks in advance for all support!