FREN 105 Chapter 9: 9.3 - 9.4

Problem 3. The curve r (t) = 《t-tanh t, secht) is called a tractrix. (a) (5 points) Show that is equal to 8 (t) ln (cosh t) (b) (5 points) Verify that r(s)-(tanh-1 (V1-e-2s)-V1-e-2s, e-s is an arc length parametrization of the tractrix. * See Section 12.5.

Solve the following electronics applications using any method you choose. Find the current l as a function of time t (in seconds), given that I satisfies the differential equation I' + R/L I = sin(2t). Where R = 550 Ohms, L = 4 Henrys, l(0) = 0. q" + R/L q' + 1/LC q = 1/L E(t) where R is resistance (in Ohms), C is capacitance (in Farads), L is the L LC L inductance (in Henrys), E(t) is the electromotive force (in Volts), and q is the charge on the capacitor (in Coulombs). Find the charge q as a function of time for the electrical circuit described. Assume that q(0) = 0 and q'(0)= 0 R = 20, C = 0.02, L = 2, E(t)=35