Relative Motion to Absolute Motion

Just a quick reminder about converting relative motion to absolute motion. Say we already have the transfer function for input acceleration to relative motion:

$sys_{rel} = \frac{\delta}{\ddot{x}_1} = \frac{x_2-x_1}{\ddot{x}_1}$

The absolute motion of the second mass can be found as

$\frac{x_{2}}{\ddot{x}_{1}} = \frac{\delta}{\ddot{x}_{1}} + \frac{1}{s^{2}}$

The derivation is as follows:

$sys_{rel} = \frac{\delta}{\ddot{x}_{1}}= \frac{x_{2}-x_{1}}{\ddot{x}_{1}}=\frac{x_2}{\ddot{x}_1}-\frac{x_1}{\ddot{x}_1}$

$\frac{x_2}{\ddot{x}_1} = \frac{\delta}{\ddot{x}_{1}}+\frac{x_1}{\ddot{x}_1}=\frac{\delta}{\ddot{x}_{1}}+\frac{1}{s^2}$

Relative Motion to Absolute Motion

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