Transient solution from a set of initial conditions

Inserting values of system parameters into equation (8.53) gives 

Compare equation (8.55) with the denominator of the standard form in equation (3.43) 

Using the standard matrix operations given in Appendix 2, equation (A2.12) 

Note that the exponential indiees are the roots of the eharaeteristie equation (8.56). (e) From equation (8.51), the transient response is given by 

For the spring-mass-damper system given in Example 8.6, evaluate the transient response of the state variables to a unit step input using 

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