2 9-5 0.1,H 100Ω 3[1-2u()] A Findi) for all t Rat (b) 10u(1) V. ン Findin...
1.[10pt] Compute the convolution X(t)* v(t). x(t) = 2u(t) – 2u(t – 2), s 2-t, 0<t<2 v(t) = { ö otherwise
Consider the circuit below, we can show: 522 10u(-1) V 2012 05H3, i(t)= 2e-8t u(t) A The steadystate inductor energy for t> 0 is 1 The initial inductor power p(0) = 16 W The steady-state inductor energy fort > O is OJ
u =<4, -5 > v=<3, 2 > | 2u – vl = ? Whole number. <7, -1, 5 >.< 2, 3, 1>=? whole number
(1 point) Solve the heat problem with non-homogeneous boundary conditions ∂u∂t(x,t)=∂2u∂x2(x,t), 0<x<3, t>0∂u∂t(x,t)=∂2u∂x2(x,t), 0<x<3, t>0 u(0,t)=0, u(3,t)=2, t>0,u(0,t)=0, u(3,t)=2, t>0, u(x,0)=23x, 0<x<3.u(x,0)=23x, 0<x<3. Recall that we find h(x)h(x), set v(x,t)=u(x,t)−h(x)v(x,t)=u(x,t)−h(x), solve a heat problem for v(x,t)v(x,t) and write u(x,t)=v(x,t)+h(x)u(x,t)=v(x,t)+h(x). Find h(x)h(x) h(x)=h(x)= The solution u(x,t)u(x,t) can be written as u(x,t)=h(x)+v(x,t),u(x,t)=h(x)+v(x,t), where v(x,t)=∑n=1∞aneλntϕn(x)v(x,t)=∑n=1∞aneλntϕn(x) v(x,t)=∑n=1∞v(x,t)=∑n=1∞ Finally, find limt→∞u(x,t)=limt→∞u(x,t)= Please show all work. (1 point) Solve the heat problem with non-homogeneous boundary conditions au ди (x, t) at (2, t), 0<x<3, t> 0 ar2 u(0,t) = 0, u(3, t) = 2, t>0, u(t,0)...
3. Given the circuit in Figure 3, find v(t) for all t>0. t=0 v(t) 4 A 20 22 60 Ω 0000 15 H 1/30 F HL
Problem # 1: Consider the circuit of Fig. 1: a) If vc(0) 8 V and i,(t) 40 S(t) mA, find Vc(s) and vc(t) fort>0 b) If ve(0) 1 V and ) 0.2 e u(t) A, find Vc(s) and v(t) fort>0 Problem #2: The circuit in Fig. 2 is at steady-state before t-0. a) Find V(s) and v(t) for t>0 b) Find I(s) and i(t) for t>0 5 S2 10 - 10u(t) V 6 H v(t) i(t). 130 F Figure 1...
8 H 2 Q iL Vs (t 22 1. vs (t) 2 V; this is a dc source. Solve using a simple circuit analysis method 2. Us (t) 2u (t) V; solve by writing and solving the differential equation for the circuit, as in Ch. 8. You = = 0 for t0. can assume that ir 2u (t) V; solve using the Thévenin method, as in Ch. 8. You can assume that i, = 0 for t< 0. 3. vg...
4) Given Variables: L1 : 0.1 H Determine the following: a1 (A/s) : a2 (A) : a3 (A/s) : a4 (A) : a5 (A/s) : a6 (A) : a7 (A/s) : a8 (A) : Find the current i(t) in the circuit, when i(0)-1A and the voltage is as shown in the graph i(t) -att a2 for Os<t<1s for 1s<t<4s for 4 s<t<9s for 9 s <t i(t) ast + a6 8 vs(V) i(t) 1 2 3 5 6789t(s)
Alpha=9 beta=3 yazarsin 1. Consider the following initial-value problem. y' = e(1+B)t ln(1 + y2), 0<t<1 y (0) = a +1 a) ( 15p.) Determine the existence and uniqueness of the solution. b) ( 15p.) Use Euler's method with h = 0.25 to approximate the solution at t = 0.5. {"
Question 4 Find i(t) for t >0 for the circuit below. 4Ω 12 V 5 H 3 A