# Does the mass of the damper affect the transfer function in a vertical mass-spring-damper?

Usually in system dynamics, I dealt with horizontal mass spring dampers. Now in my advanced class I am dealing with vertical mass spring dampers. So a spring is hanging from the ceiling with a mass connected, and then the damped is under the mass. The damper is in some sort of oil and that is creating the "damping" effect.

In this problem, the spring is assumed to be negligible mass, but the damper has a mass, along with the weight that is acting as the mass.

I know that for a mass spring damper system (when its horizontal), the transfer function is $$H(s)=\frac{\omega_{n}^{2}}{s^{2}+2\zeta\omega_{n}s+\omega_{n}^{2}}$$

But now the mass of the weight and damper are acting on this system. So does that affect the transfer function?

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