Moving Mass

Figure B.1 depicts a free mass driven by an external force along
an ideal frictionless surface in one dimension. Figure B.2
shows the *electrical equivalent circuit* for this scenario in
which the external force is represented by a voltage source emitting
*volts*, and the mass is modeled by an *inductor*
having the value *Henrys*.

From Newton's second law of motion ``'', we have

Thus, given

- Laplace transform of the driving force ,
- initial mass position, and
- initial mass velocity,

If the applied external force is zero, then, by linearity of the Laplace transform, so is , and we readily obtain

To summarize, this simple example illustrated use the Laplace transform to solve for the motion of a simple physical system (an ideal mass) in response to initial conditions (no external driving forces). The system was described by a differential equation which was converted to an algebraic equation by the Laplace transform.

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