Problem Set 11

Problem Set 11 - MASSACHUSETTS INSTITUTE OF TECHNOLOGY...

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PS08-1 MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Physics 8.02 Spring 2008 Problem Set 11 Due: Wednesday, April 30 at 11 am. Hand in your problem set in your section slot in the boxes outside the door of 32- 082. Make sure you clearly write your name, section, table, group (e.g. L01 Table 3 Group A) Problem 1: Key Identity (10 points) Show that ( ) m cos sin cos At Bt Q t ω ωω φ + =+ , where () 12 22 m QA B , and 1 tan ( / ) B A =− . Problem 2: (10 points) For the underdamped RLC circuit, 2 4 R LC < , let ( ) 14 LC R L γ and 2 RL α = . (a) Show by direct substitution that the equation 2 2 0 d Q dQ Q LR dt dt C = ++ has a solution of the form cos ( ) t Qt Ae t = + (b) Denote the current by cos( ) t dQ t It F e t dt φβ == + + Find the constants F and β in terms of R , L and C as needed.
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PS08-2 Problem 3: (10 points) Review Experiment 7: Undriven RLC Circuits ; Read Experiment 8: Driven RLC Circuits Consider the circuit at left, consisting of an AC function generator ( 0 () sin( ) Vt V t ω = , with V 0 = 5 V), an inductor L = 8.5 mH, resistor R = 5 Ω , capacitor C = 100 μ F and switch S .
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Problem Set 11 - MASSACHUSETTS INSTITUTE OF TECHNOLOGY...

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