Mechanical Systems

In mechanical systems, springs, and masses are akin to the roles of inductors and capacitors in electrical networks, with the energy-dissipating function of a viscous damper corresponding to that of electrical resistance.

The forces acting on the mass include an applied force moving in the same direction and the forces from the spring, viscous damper, and acceleration acting against it.

Like the RLC network, translational mechanical systems are defined by a unique differential equation formulated by applying Newton's law which mandates that the sum of all forces acting on the mass must equal zero.

Further, the Laplace transform is used on the equation under zero initial conditions. This expression, when simplified, yields the transfer function.

The components in rotational mechanical systems mirror those of translational systems but experience rotation.

These are managed similarly to translational ones, with torque substituting force, angular displacement replacing translational displacement, and inertia replacing the mass.

In the second-order differential equation for the rotational system, the Laplace transform is applied and then further simplified to yield the transfer function.