Problem 1 reference: 4. 110 points Consider the dynamical system given in Problem 1 (a)-ii. (a)...
Problem 1 (20 points) Consider the differential equation for the function y given by 4 cos(4y) 40e 2e) cos(8t)+5 eu 2t) sin(8t)/ - 12e - 0. 8 sin(4y) y a. (4/20) Just by reordering terms on the left hand side above, write the equation as Ny + M 0 for appropriate functions N, M. Then compute: aN(t, y) ayM(t, y) b. (8/20) Find an integrating factor If you keep an integrating constant, call it c (t) N and M M,...
Verify that Prn (cos θ) solves sin θΟθ (sin ea, Θ) + (E(1 + 1) sin2 θ-m2) Θ 0. Use that pr(z)-(1-z2 )T (4), Pr(r) with Pr(z) a Legendre polynomi 1 Verify that Prn (cos θ) solves sin θΟθ (sin ea, Θ) + (E(1 + 1) sin2 θ-m2) Θ 0. Use that pr(z)-(1-z2 )T (4), Pr(r) with Pr(z) a Legendre polynomi 1
Problem 4. (16') If an object moves in the p tor r(t). If at t 0 we have .. 2 cos(2r)). Determine r(O) (3,-3. 4). and the velocity vector is given as r() the position vector r(t) sin(2t), 3t
Last Name: Page Problem #2 (35 Points) Given The motion of a particle P which coincides with the robot's gripper hand at point A is defined by the relations where t is expressed in seconds. Please note that kı, k2, and ks are constants which are greater than zero. For the initial condition, the particle has an angle of 0-0° when-0 sec. So, when t 2 sec, Find: a) The "script" values for radial and transverse coordinates, that is, r,t,i,...
Problem #2 (35 Points) Given The motion of a particle P which coincides with the robot's gripper hand at point A is defined by the relations r-|kıBeos(K2O) ] m and θ (k31) rad, where t is expressed in seconds. Please note that ki, k2, and ks are constants which are greater than zero. For the initial condition, the particle has an angle of 0-0 when t 0 sec. So, when t 2 sec, Find a) The "script" values for radial...
QUESTION 4 (4.1) Consider the variational problem with Lagrangan function 2r Sin t and endpont conditions z(0) 0, z(*/2) = 1 (a) Find the smooth extremal of the gven vanational problem (7) (6) (b) Compare the value of the fundamental integral dt along an extremal between those two endpoints wnth the value along the curve z 1-cost through the two points Hint: You may use integration by parts and also remember that cost-(1+cos 2t), ant (1-cos 2t) and sin 2t...
-1-1 arctan n n" n!5* (c) Find the interval of convergence and radius of convergence for )0301 i )e-3r) (d) Use the geometric series to write the power series expansion for i. f(1)- 2-4r, centered at a = 0. i.)4 centered at a-6. (e) Write the first 4 nonzero terms of the Maclaurin expansion for i, f(z) = z2 (e4-1) ii. /(x) = cos(3r)-2 sin(2x). (0) Use the Taylor Series definition to write the expansion for f(a)entered at (8) Use...
Example 10.5-1 (See Example 10.5-1 in the textbook for the solution to a similar problem.) 68Ω i(t) yso) 6.0H This circuit is at steady state. The input to this circuit is the voltage source voltage, vs(t), given by Vs(t) = 22cos(12t + (35° ) v The steady-state mesh current, (t), can be expressed as i(t)-A cos(12t + θ) mA 1809. Determine the values of the constants A and θ: where A and θ are constants such that A > 0...
Problem 5. Prove that parametric equations: x a-cosh(s) (a > 0) or back half(a < 0) of hyperboloid of one sheet: Χ t), y b-sinh(s) cos (t) zc-sinh(s) sin( t), (x,y,z) lies on the front half L" a2 b2 c2 Problem 6 What graph of this Compute the arc length : rit)- < sin t, cos t, 2Vt', when 0<t < function: a) Compute the arc length : re)-3cos(9) and 0 < θ < π/2 b) Problem 7. Find parametric...
Assignment 4 - Vector Functions: Problem 7 Previous Problem Problem List Next Problem (1 point) Consider the curve r = (e-44 cos(—2t), e-4t sin(–2t), e-4). Compute the arclength function s(t): (with initial point t = 0). 2(14)^(1/2)*(1/4-(e^(-4t))/4) Preview My Answers Submit Answers You have attempted this problem 1 time. Your overall recorded score is 0%. You have unlimited attempts remaining.