E8. 14 a) Find Vrms if v(0)-2+4cos(3t-30')+ 10sin(6t+ 60) v b) Find Irm, if i()-4cos(3t+30)+ 10sin(3t...
1. A LTI system has the frequency response function 0, all other o Compute the output y(t) resulting from the in put x(t) given by (a) x(t) -2-5cos(3t)+10sin(6t-jx/3)+4cos(12t-x/4) (b) x(t) = 1 + Σ- cos(2kt ) k-l (c) x(t) is the periodic pulse train signal shown below (repeats beyond the graph) 0.5 0.5 5 t (second) Hint: Refer to lecture 10 note. For (c), find the Fourier series coefficients of x(t) first. 1. A LTI system has the frequency response...
3) Givenr"(t) = (6t + 4)+(-sint)i + (-4cos(2t))k, and r'O) = 0 and r(0) = 41 -1+k a) find r(t). 4) Givenf (x,y) = 6xły – yex-1 a) Find Vf(x,y). Show all support work! b) Find the direction of maximum increase of f(x,y) at the point (1,-1).
3) (20 points) For the circuit in figure below, find i(t) 30 12 cos(6t +30) A 16 0 i(t) 50 sin(2t) V
the velocity of a particle traveling in a straight line is given by v=(6t-3t^2)m/s, where t is in seconds, if s=0 when t= 0. determine the particles deceleration and position when t=3s. how far has the particle traveled during the 3s time interval and what is its average speed?
4. Consider a sinusoidal voltage signal of the form: v(t)=10sin(2(pi)1000t) Determine: a. average value of v(t) b. maximum value of v(t) c. minimum value of v(t) d. RMS (root mean square) value of v(t) Now assume that this signal is driving a 25Ω load. Determine: e. average power dissipated in the load f. maximum instantaneous power dissipated in the load g. Minimum instantaneous power dissipated in the load Also, provide: h. Frequency in Hz i. Period, in ms j. frequency...
let two vectors be a(t) = e^t i + (sin 2t) j + t^3 k and b(t) = (e^-t , cos 3t, - 2 t^3) in euclidean three space R^3. Find d/dt [a(t) * b(t)].
2. Find the Laplace transform of the following functions (a) f(t)3t+4 (b) cos(2Tt) (c) sin(2t T) (d) sin(t) cos(t) "Use Trig. Identity" (e) f(t) te 2t use first shifting theorem
Please do the problem if you can do ALL parts. t-0 a SW1 SW2 0.5 Ω 2 1Ω V. R3 20 A T v(t) 0.5 F 0.5 H 0 Find the initial current i(0) through the inductor and the initial voltage v(0) across the capacitor at t 0. b. Write a node equation at node a fort2 0. c. Represent v(t) as a function of i(t) on the series connection of R2 and L. Find dv(t)/dt. Derive a second-order differential...
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...
Problem 2: Find the nodal voltages and the current I. 30 40 V 60