Recall that the differential equation for the instantaneous charge q(t) on the capacitor in an LRC-series circuit isMY NOTESASK YOUR TEACHER+ Rda= E(t).+dt 2dtCSee this excerpt about LRC-series circuits. Use the Laplace transform to find q(t) when L=1 h, R = 20 N, C = 0.005 f, E(t) = 160 V, t > 0, q(0) = 0, andi(0) = 0.q(t) =What is the current i(t)?i(t)

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Answered: Recall that the differential equation…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Suppose a pendulum of length L meters makes an angle of 0 radians with the vertical, as in the figure. It can be shown that as a function of time, 0 satisfies the differential equation + dt? sin 0 = 0, where g = 9.8 m/s is the acceleration due to gravity. For 0 near zero we can use the linear approximation sin(0) z 0 to get a linear differential equation - 0 = 0. dt? Use the linear differential equation to answer the following questions. do (a) Determine the equation of motion for a pendulum of length 2 meters having initial angle 0.2 radians and initial angular velocity 0.2 radians per dt second. O(t) = radians (b) What is the period of the pendulum? That is, what is the time for one swing back and forth? Period = seconds
A tank contains 460 gallons of water and 45 oz of salt. Water containing a salt concentration of 1/7(1+1/4sint) oz/gal flows into the tank at a rate of 9 gal/min, and the mixture in the tank flows out at the same rate. The long-time behavior of the solution is an oscillation about a certain constant level. What is this level? What is the amplitude of the oscillation? Round the values to two decimal places. Plz correct solution.
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55. Figure 8 shows a circuit consisting of a resistor of R ohms, a capacitor of C farads, and a battery of voltage V. When the circuit is completed, the amount of charge q(t) (in coulombs) on the plates of the capacitor varies according to the differential equation (t in seconds) dq R= dt where R, C, and V are constants. (a) Solve for q(t), assuming that q (0) = 0. (b) Sketch the graph of q. (c) Show that lim q(t) = CV. t-00 (d) Show that the capacitor charges to approximately 63% of its final value CV after a time period of length t is called the time constant of the capacitor). RC (t FIGURE 8 An RC circuit.

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