B. PEIKARI Exercises find v(t) for t >=0


B. PEIKARI Exercises find v(t) for t >=0 fend fn tyo Uit) Im he Cncuitahsuun, UI0)=...
4. a) Find Tou(t) if w=100. ans: Ju: 0767 Lugo b) Find To for w=0, w=50, w=200, w=500. ans: 1; 0.312279 0.45 -13° 0.20-710.. c) Plot the magnitude of to as a function of w.. d) Plot the phase of to as a function of w.. ter . Vit) 1610-27 v(t) = Coswt
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
3. For each n E N let fn : (1, 0) -+ R be given by f/(x) = Find the function f : (1, 0) - R to which {fn} converges pointwise. Prove that the convergence is not uniform
3. For each n E N let fn : (1, 0) -+ R be given by f/(x) = Find the function f : (1, 0) - R to which {fn} converges pointwise. Prove that the convergence is not uniform
3. The sequence (Fn) of Fibonacci numbers is defined by the recursive relation Fn+2 Fn+1+ F for all n E N and with Fi = F2= 1. to find a recursive relation for the sequence of ratios (a) Use the recursive relation for (F) Fn+ Fn an Hint: Divide by Fn+1 N (b) Show by induction that an 1 for all n (c) Given that the limit l = lim,0 an exists (so you do not need to prove that...
(a) In the network in the accompanying figure,
find i(t) for t > 0.
(b) If
vC1(0–) = – 13 V, calculate
vC2(0–).
Please round all numbers to 3 significant digits.
(a) In the network in the accompanying figure, find i(t) fort > 0. (b) If Vc1(0-) = - 13 V, calculate vc2(0-). + °C (t) HE 0.8 F + 13e-5łu(t) v 0.2Fvc2(t) Please round all numbers to 3 significant digits. (a) i(t) = *e Edit A (b) Vc2(0-) =...
6.3 Exercises In Exercises 1-5 find the current in the RLC circuit, assuming that E(t) = 0 fort > 0. 1. R = 3 ohms; L = 1 henrysC = .01 farads; Q. = 0 coulombs, 10 = 2 amperes. 11. Show that if E(t) = U coswt +V sin wt where U and V are constants then the steady state current in the RLC circuit shown in Figure 6.3.1 is w?RE(t) + (1/C - Lw?) E' (t) I where...
4. For each n EN let fn: [0,1]R be given by if xE(0, otherwise fn(x) = (a) Find the function f : [0, 1] R to which {fn} converges pointwise. fn. Does {6 fn} converge to (b) For each n EN compute (c) Can the convergence of {fn} to f be uniform?
4. For each n EN let fn: [0,1]R be given by if xE(0, otherwise fn(x) = (a) Find the function f : [0, 1] R to which {fn}...
I) After being closed a long time, the switch opens at t-0. Find: (a) v.(0) (b) İd0'), (c) dv/dt(0) (d) v1(0), (e) İL(0+), (f) dv/dt(0) (20%) t=0 VL- 2 Ohms 3 H 1 F + 12 V ( ic 寸
Consider the following second order PDE Uit – 9Uxx = 0, 0<x< < t > 0, (A) and the following boundary value/initial conditions: Ux(t,0) = uſt, 5) = 0, t>0, u(0, x) = 44(0, x) = 4 cos’ x, 0<x< (BC) (IC) for the function u= u(t, x). a. (5 points) Find ordinary differential equations for functions T = T(t) and X = X(x) such that the function u(t, x) = T(t)X(x) satisfies the PDE (A). b. (5 points) Find...
Let V be a vector space, and ffl, f2, fn) c V be linear functionals on V. Suppose we can find a vector vi e V such that fl (v) 6-0 but £2(v)-6(v) = . . .-m(v) = 0. Similarly, suppose that for all 1 i < n we can find vi є V such that fi(vi) 6-0 and fj (vi)-0 for alljöi. Prove that {fL-fa) is were linearly independent in V ly independent in V * . Prove also...