For the system below, use the Newton Method to find equivalent stiffness, equivalent

mass, and natural frequency. Do not try to prove that the force of gravity is cancelled by

the springs' initial deformations. If the system is designed in a way that the force of

gravity is cancelled, don't include the force of gravity in the Dynamic FBD$.$

Consequently, there is no need to draw the Static FBD nor calculate the initial

deformation of the springs.

Hints: All the systems have one DOF even though some have more than one mass. For

the ones with more than one mass.

Define one generalized coordinate for each mass, then find the relationship between

the generalized coordinates so later you can eliminate the extra generalized coordinates

and write the final solution as a function of only one generalized coordinate.

One FBD and one differential equation are necessary for each mass.

Plug the equations into each other to eliminate the unknown reaction forces, like the

tension force of belts. This way you will have only one ODE at the end.