ma266-proj2-f10

# ma266-proj2-f10 - ω and discuss what appears to happen to...

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Computer Project 2. RLC Circuits Goal: Investigate the charge on a capacitor in an RLC circuit with varying voltage. Tools needed: ode45 , plot Description: If Q ( t ) = charge on a capacitor at time t in an RLC circuit (with R , L and C being the resistance, inductance and capacitance, respectively) and E ( t ) = applied voltage, then Kirchhoﬀ’s Laws give the following 2 nd order diﬀerential equation for Q ( t ): LQ 00 ( t ) + R Q 0 ( t ) + 1 C Q ( t ) = E ( t ) ( * ) E ( t ) L C R Questions: Assume L = 1, C = 1 / 5, R = 4 and E ( t ) = 10 cos ωt . 1. Use ode45 (and plot routines) to plot the solution of ( * ) with Q (0) = 0 and Q 0 (0) = 0 over the interval 0 t 80 for ω = 0 , 0 . 5 , 1 , 2 , 4 , 8 , 16. 2. Let A ( ω ) = maximum of | Q ( t ) | over the interval 30 t 80 (this approximates the amplitude of the steady-stat solution). Experiment with various values of
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Unformatted text preview: ω and discuss what appears to happen to A ( ω ) as ω → ∞ and as ω → 0. Also, interpret your ﬁndings in terms of an equivalent spring-mass system. Remark: There is an analogy between spring-mass system and RLC circuits given by: Spring-mass system RLC circuit mu 00 + cu + k u = F ( t ) LQ 00 + R Q + 1 C Q = E ( t ) u = Displacement Q = Charge u = Velocity Q = I = Current m = Mass L = Inductance c = Damping constant R = Resistance k = Spring constant 1 /C = (Capacitance)-1 F ( t ) = External force E ( t ) = Voltage...
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