Question

Determine the time function, s-domain function and transfer function

Answer 1

Solution via Transfer Function

Before starting this section make sure you understand how to create a transfer function representation of a system.

Zero input and zero state solutions of a system can be found if the transfer function is known, though the transfer function is more commonly used for the zero state response.  We will first develop the transfer function for a system, and then solve for the zero state and zero input solutions. 

The system shown is a simplified model of a part of a suspension system of a wheel on a car or motorcyle.  The mass, m, represents the weight of the vehicle supported by the wheel, and the spring and dashpot represent the suspension system.  For our purposes let m=500 kg, k=3000 N/m, b=2500 N-m/s.