Page 393 - Schaum's Outline of Theory and Problems of Signals and Systems
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STATE SPACE ANALYSIS [CHAP. 7
In matrix form
Consider the mechanical system shown in Fig. 7-4. It consists of a block with mass m
connected to a wall by a spring. Let k, be the spring constant and k, be the viscous
friction coefficient. Let the output y(f) be the displacement of the block and the input
x(f) be the applied force. Find a state space representation of the system.
By Newton's law we have
The potential energy and kinetic energy of a mass are stored in its position and velocity. Thus,
we select the state variables q,(t) and q2(t) as
Then we have
y4
y(0
Fig. 7-4 Mechanical system.
