Modelling of mechanical system in control system problems

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Draw free body diagram of the system
Free body diagram is obtained by drawing each masses separately and then mark all the forces acting on that body
Opposing forces are in opposite direction of applied force
Applied force and displacement are in same direction
For each free body diagram write one differential equation by equating the sum of applied forces to the sum of opposing forces
Take Laplace transform to convert differential equation into algebraic equation
Then rearrange the S- domain equation to eliminate unwanted variables and then obtain the transfer function which is the ratio of output by input.