Consider three functions x(t), v(), and at), such that dx dt dv - alt) dt The...
15. Suppose y= V5x+1 where x and y are functions of t. (a) If dv/dt = 10, find dy/dt when x= 3. 6) If dyldt = 7, find dx/dt when x = 7.
Consider the following system. dx dt dy dt 5 x + 4y 2 3 =X - 3y 4 Find the eigenvalues of the coefficient matrix Alt). (Enter your answers as a comma-separated list.) Find an eigenvector for the corresponding eigenvalues. (Enter your answers from smallest eigenvalue to largest eigenvalue.) K K₂ = Find the general solution of the given system. (x(t), y(t)) =
dx dt 1. For the circuit below determine: a) The initial conditions: iz(0+), dix(0*), v(0+), dv(0+) b) The circuit differential equation and solve for iz(t), t 2 0 (No credit for Transform techniques) ix VI 102 422 + lo 5+10u(t) 10 H 1/4 F V
Consider the initial value problem given below dx -2 +t sin (x), dt x(0) 0 Use the improved Euler's method with tolerance to approximate the solution to this initial value problem at t 1. For a tolerance of e-0.01, use a based on absolute error stopping procedure Consider the initial value problem given below dx -2 +t sin (x), dt x(0) 0 Use the improved Euler's method with tolerance to approximate the solution to this initial value problem at t...
Given the first order equation describing the circuit... 4(dv/dt)+v=10 Find the time constant Find the final value of the voltage If v(0)=2 the function describing v(t) for all time.
(6). The quantities x(t) and y(t) satisfy the simultaneous equations dt dt dx dt where x(0)-y(0)-ay (0)-0, and ax (0)-λ. Here n, μ, and λ are all positive real numbers. This problem involves Laplace transforms, has three parts, and is continued on the next page. You must use Laplace transforms where instructed to receive credit for your solution (a). Define the Laplace Transforms X(s) -|e"x(t)dt and Y(s) -e-"y(t)dt Laplace Transform the differential equations for x(t) and y(t) above, and incorporate...
Given that no-5 and dv(0)/dt-10, solve-it2t) + 6U-30 e-tu (t). + 5 -t 2t V(t) is calculated as | e3 u(t)
Construct a Liapunov function on the form V(x,y) = ax2 + cy2 for the nonlinear system dx dt dy dt 3 山 一一 and deduce that the critical point at the origin is asymptotically stable. Construct a Liapunov function on the form V(x,y) = ax2 + cy2 for the nonlinear system dx dt dy dt 3 山 一一 and deduce that the critical point at the origin is asymptotically stable.
Starting with an expression for U(S.V), show that m(V) = (dU/dV)T is given by Tt(v)= (dp/dT)V-P.
aliasing? A continuous-time system is given by the input/output differential equation 4. H(s) v(t) dy(t) dt dx(t) + 2 (+ x(t 2) dt (a) Determine its transfer function H(s)? (b) Determine its impulse response. (c) Determine its step response. (d) Is the stable? (a) Give two reasons why digital filters are favored over analog filters 5. (b) What is the main difference between IIR and FIR digital filters? (c) Give an example of a second order IIR filter and FIR...