Use circuit analysis to solve for Vx(t) in the form of f(t) = [ f(0+) – f(∞) ] e^(-t/τ) + f(∞)
Where u(t) is a step function
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Use circuit analysis to solve for Vx(t) in the form of f(t) = [ f(0+) –...
Use the Laplace transform to solve the given integral equation. f(t) + t (t − τ)f(τ)dτ 0 = t
1-5 im struggling pls help Applications of Solutions by Laplace Transform Given L I (0) = 0 for t > 0. Solve for the current I (t) +臘娃q=E(t), w th L-1h,R= 20 ohms, C=0.005 f, E(t) = 150V, q(0)=0and 1. de? Find the charge q(t) in an RC series circuit when q(0)-0 and E(t) = E e-kt, k > 0. Consider both when k 2. and when k = RC. Translations on the t-Axis Using Unit Step Function Find the...
5. Express f(t) using the unit step function an then use the Laplace Transform to solve the given IVP: y' + y = f(t), y(0) = 0, where f(t) = So, ost<1 15, t21
Applied Mathematics Laplace Transforms 1. Consider a smooth function f(t) defined on 0 t<o, with Laplace transform F(s) (a) Prove the First Shift Theorem, which states that Lfeatf(t)) = F(s-a), where a is a constant. Use the First Shift Theorem to find the inverse trans- form of s2 -6s 12 6 marks (b) Prove the Second Shift Theorem, which states that L{f(t-a)H(t-a))-e-as F(s), where H is the Heaviside step function and a is a positive constant. Use the First and...
Find i(t) for t> 0 in the op amp circuit of Fig. P4. (u(t) is unit step function. It is 1 for t> 0 and 0 for t<0.) 1/6F It 3 Ω 212 + 2 u(t) V 1/6 F 10 Ω Figure P4
4. Find vx(t) in the time domain in the following circuit. (12 points) 0.005 F 100 0.1 H Mmm 100 cos 40 v v (0) 40 cos (401 - 30) V 0.2 H 50 5. Find I in the circuit below using nodal analysis. Hint: Reduce the number of nodes first. (10 points) 6 12/0v +-20 3/10A 6/o v
3 Draw the circuit at too and force i(0*) and ve(0*). Then solve for v(0*) and 4c(O*). Find the second intial condition given as 2 (7) 3- Draw the circuit at tm Replace the inductor with short circuit, and the capecitor with open circuit Then sove for 4i (o) and v (oo). Once the three values are obtained, you have two initial conditions to solve for A and B. In this lab, you will build a parallel RLC circuit shown...
Solve the IVP y' + y = f(t), y(0) = 0, where f is the 27-periodic function given by f(t) -1, 0<t<T, <t<21, f(t) = f(t + 27).
How would you find v(t) ? 1. Solve for the voltage v(t) in the circuit shown below when t = 0.73 ms. The voltage source is e(t) = 8 Vu(t), where u(t) is the unit step function. The component values are: R1 = 3 k.2, R2 = 4k.2. R3 = 2 k2, R4 = 10 k.2, R; = 1 k.2 and C = 0.22uF. RA w R1 w R2 e(t) ( R57 Ra} V(t) v(t) =
4) Use the laplare trans form to solve the Iupy" zylty = f (t), yo) = 1, y'(o) - I, where So, ta3