This can be seen in the graphs for question one whereas w increased the maximum

This can be seen in the graphs for question one

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0. This can be seen in the graphs for question one, whereas w increased, the maximum value of |Q(t)| grew increasingly smaller. Another example can be seen below (left image) for w = 50 and the Max. |Q(t)| = 0.00399. Overall, as w approaches infinity, the amount of stored charge in the circuit goes to zero. As w à 0, the value of A( w ) à 2. This can be seen in the first graph in question one which set w = 0, thus generating a maximum value of |Q(t)| of 2. As the value of w get smaller, the charge over time becomes less stable. However, the maximum value, despite this instability, is two. This can be seen above (right image) for w = 0.001. Overall, as w approaches zero, the stored charge in the circuit is 2. The results of the RLC circuit function is also analogous to the spring-mass system worked on previously. The value of w represents an oscillating voltage for an RLC circuit but represents an oscillating external force for the spring-mass system. When w approaches zero, there is a constant voltage acting on the system and a constant charge is maintained in the circuit. Similarly, there is a constant external force acting on the spring-mass system which would create a constant displacement for the system. As the value of w approaches infinity, the stored charge in the circuit and the amplitude for the spring-mass system are both zero. This is primarily due to the fact that the external force and the voltage have value of zero due to the value of t being infinitesimally small so the average value taken results in the no oscillation for force and voltage.
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  • Spring '09
  • RLC, Inductor, Electronic oscillator

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