MIT2_017JF09_p10

# MIT2_017JF09_p10 - 10 SIMULATION OF A SYSTEM DRIVEN BY A...

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10 SIMULATION OF A SYSTEM DRIVEN BY A RANDOM DISTURBANCE 17 10 Simulation of a System Driven by a Random Dis­ turbance 1. Simulate the second-order system: x + ax + bx = d ( t ) with a = 0 . 4 and b = 2 . 25. Figure 1 below shows responses to the same disturbance d ( t ) for all the three values of a . Note that because the phases are generated from random numbers, your figure might not look like this, although the size of the response should be similar. Also, the component periods repeat within sixty seconds, so d ( t ) repeats itself in this graph. 2. From the graph, about what is the ”significant height” of the motion? The significant height of the response with a = 0 . 4 is around two units. 3. What is the effect of reducing or increasing the damping in this system, say a = 0 . 2 and then a = 1 . 0? The response of the system is clearly strongly dependent on the damping ratio: the oscillations are much larger as the damping ratio gets smaller. This is no surprise since the undamped natural frequency is 1.5, near where the disturbance

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