Condsider the ODE d2 x () + 32 x (t) = F (t) where the forcing function is given by the Fourier series with co -1, c18, Assuming a particular solution of the form find and enter the exact values of an and bn requested below Cn cos (n t), 3p (t)-a0 + Σο.1 (an cos (n ) + bn sin (n t)) Condsider the ODE d2 x () + 32 x (t) = F (t) where the forcing function...
Condsider the ODE d2 1 (t) + 50 x (t) = F(t) dt2 where the forcing function is given by the Fourier series F(+) = 0 +21 on sin (nt) with co = 9, c1 = 10, ... Assuming a particular solution of the form Ip (t) = a0 + Anal (an cos (n t) + bn sin (nt)) find and enter the exact values of an and bn requested below. 20 41 == 61 - 10
d1= 3 and d2= 2 Question 1 ch- 3, d2 - 2 (a) Find the most general solution u(x, y) of the two PDEs Lt +1) y cos y +(di +1)x cos ((d, +1)xy)+2x d2 (b) Find the solution that satisfies initial condition u(0,0) Question 1 ch- 3, d2 - 2 (a) Find the most general solution u(x, y) of the two PDEs Lt +1) y cos y +(di +1)x cos ((d, +1)xy)+2x d2 (b) Find the solution that satisfies...
QUESTION 11 Solve 27sin(t)*cos(t) = -12sin(t) for the smallest non-negative solution QUESTION 12 Solve cos(x) = -2sin(x) for the smallest non-negative solution QUESTION 13 Solve 14sin(t)*cos(t) = -6cos(t), for the smallest non-negative solution, where t is between 0 and 2pi QUESTION 14 Solve sec(4x) - 2 = 0 for the smallest non-negative solution QUESTION 15 Solve cos(x) = 6sin(x) for the smallest non-negative solution
II. DERIVATIVES A) Given x A cos(ot), find dt d2 χ dt2 B) Is A cos(wt) a solution tox? Why or why not? d2x dt2 C) is χ-A cos(5t) a solution to--:-3x ? Why or why not? dt2
Verify that x(t) = C1et + C2 is a solution to x" − x' = 0. Find C1 and C2 so that x(t) satisfies x(0) = 10 and x'(0) = 100. Sketch a graph of the solution x(t) given the calculated values of C1 and C2.
(i) Consider the wave Ē(7,t) = Ło cos(wt – k ), where Ē, is a fixed vector. Determine the relation between w and k = \KI SO that Ē(7,t) is a solution of the wave equation -27 182 VPE = 2 ət? - What is the direction of propagation of the wave? ii) Show, by substitution of Ē(7,t) in the appropriate Maxwell's equation, that K· Ē= 0. iii) Assuming that the magnetic field B(7, t) = B, cos(wt – K:1),...
The wave functions for two harmonic waves are given by D1(x,t) =(0.3m)sin(2.0x−3.0t), D2(x,t) =(0.3m)sin(2.0x−3.0t+π/2) where x is in metres and t is in seconds. If the resultant wave is expressed as Dresultant(x,t)=(C1)cos(C2)sin(C3x+C4t+C5) what are the constants? Please enter numeric answers, not equations and/or variables. C1/C2/C3/C4/C5 =? Include units.
for the following parabolic PDEs heat equation for one variable d2/dx² u(x,t) = d/dt u(x,t) . Where u(0,t)=0 , u(1,t)=0 , u(x,0)=sinπx . Complete using crank nicolson method . With h=0.2 , k=0.02
Consider two random processes X(t) and Y(t) defined as X(t)=Acos(wot+z), Y(t)=Bsin(wo+z) where A and B and wo are constants and z is a random variable that is uniformly distributed between 0 and 2pi. find the cross-correlation function of X(t) and Y(t). If both X(t) and Y(t) were wide sense stationary , could they also be jointly wide sense stationary?