8. The position vector r of a point P is a function of the time t and r satisfies the vector differential equation d2r dr 2k (k2 n2)r g, dr2 where k and n are constants and g is a constant vector. Solve dr a and dt this differential equation given that r v when t = 0, a and v being constant vectors Show that P moves in a plane and write down the vector equation of this plane...
2. Consider the circuit shown below. V, R, (a) Identify the essential nodes. (5 pts) 0, node (b) Identify the 'Rule #0. nodes. Derive an expression for each" Rule # voltage. (5 pts) (c) Employing nodal analysis, derive an expression for all essential node voltages (excluding 'Rule #0, nodes). (20 pts) mploying nodal analysis, derive an expression for any non-essential node voltages (excluding "Rule #0, nodes). (10 pts) e) Calculate a value for Vi, V'2, and Vs. Assume that Ri-3...
2.- Let r(t) = (121,842/2, 31) and let (t) be the arc length function of r() based at t=0. Calculate 8(t) as an elementary formula in t. You may assume that t > 0.
Match each given vector equation with the corresponding curve. y4 0 b a (0, 1,0) (1,0,0 , 1,0 d C 2 A (0,0. 2 y- r(t)= (, ? r(t) (sin (t),t) r (t) (t, cos (2t), sin (2t)) ? v r (t) (1 +t,3t,-t) r (t) (t)i-cos (t)j+sin (t) k =COS r(t)=i+tj+k r(t) i+tj+2k r(t)= (1,cos (t).2sin (t) Match each given vector equation with the corresponding curve. y4 0 b a (0, 1,0) (1,0,0 , 1,0 d C 2 A...
2. (25 pts) For the block diagram shown below. a) Let d(t) = 0 and r(t) =2t. Find K so that the steady state error e=0.3 b) Find the steady state errores when K-5, R(S)=1/s, D(s)=0. c) Find the steady state value of c(t), when D(s)=3/s” and R(s)0 D(s) C(s) R(5) 5+ 2 (s + 1)(s + 3)
(a) Solve the initial value problem 2" +2r' + r = 8(t - 2), z(0)=1, 2'0) = 2 (b) Consider the initial value problem -2 -5 z(0) = 3 Find ö(t), writing your answer as a single vector. k 2 k 0 1] (c) Consider the matrix 0 -2 k 3 i. Compute the determinant. ii. For what value(s) of k does A exist? iii. For what value(s) of k does the linear system A7 = 7 have nontrivial solutions?...
please solve step by step. calculate v, for t > 0 i = 8 u(t) A 212 2 H PIH ce PROBLEMA 16.6
QUESTION 1 5 points Save Answer A resistor R = 2k Ohms has a voltage V = 15 Volts. What is the current I through the resistor? Express your answer in mA. QUESTION 2 5 points Save Answer Three resistors are connected in series: R1 10k Ohms, R2 = 17k Ohms, R3 = 32k Ohms. A DC voltage source ( Volts) is connected across the three resistors. Determine the current I in mA. 7 QUESTION 3 5 points Save Answer...
Values of v()/V = -1/ IR + (1)/V V R T 21 31 0.36788 0.13534 0.04979 0.01832 0.00674 ST Figure 1: A source free RC circuit. Table 1: values of the exponential term for different t Observe from the table 1 that the smaller the time constant, the more rapidly the voltage decreases, that is, the faster the response. This is illustrated in Fig. 2. A circuit with a small time constant gives a fast response in that it reaches...
PeoB.# 3(25%) 5k Ws 36 2c lokg Kadooo fun c-400 N-s/ F(t)= 300 Sin (200) r=o.im EVALUATE THE STEADY Bu FCE STATE RESPONSE Oss(t) w 32k