2. Verify that the matrix sint coste cos t | Φ(t)= -sin t -3et is a...
cos θ cos φ sin φ sin θ, (Beats) Using the trigonometric identities cos(θ verify that φ) (β a) 2 (19) cos ot - cos Bt 2 sin A spring-mass system has an attached mass of 4 g, a spring constant of 16 g/s* and a negligible friction. It is subject to a force of 4 cos(2.2t) down- ward, and is initially 0 at rest. Determine the subsequent motion. Using (19) from Exercise 11, rewrite the solution as the product...
e-27 2. Calculate L et sint+e-2t cos st sint+e-2 cos 3t+t%e3+ + ✓at ec [e*sin U2n(t) sin 2t sin 21
16, Let x: U R2-, R, where x(8, φ) (sin θ cos φ, sin θ sin φ, cos θ), be a parametrization of the unit sphere S2. Let and show that a new parametrization of the coordinate neighborhood x(U) = V can be given by y(u, (sech u cos e, sech u sin e, tanh u Prove that in the parametrization y the coefficients of the first fundamental form are Thus, y-1: V : S2 → R2 is a conformal...
Let F(x, y, z) = sin yi + (x cos y + cos z)j – ysin zk be a vector field in R3. (a) Verify that F is a conservative vector field. (b) Find a potential function f such that F = Vf. (C) Use the fundamental theorem of line integrals to evaluate ScF. dr along the curve C: r(t) = sin ti + tj + 2tk, 0 < t < A/2.
If one eigenvalue of a 2 by 2 matrix E2x2 is 1 = 7 and a corresponding eigenvector of is ( 2) , then the general solution of the system ODES: = (t) = E2x2 f(t) cost sint is ä(t) = C: + C2 sin cost can't be determined. Solving the system requires additional information sint COS is 8(t) + C2 pot cost sint cost sint is i(t) = C: + C2 sint COS
Rewrite-2 sin(x) + 1 cos (z) as A sin (z + φ) Preview A- Preview Note: φ should be in the interval-π < φ < π
The system of non-linear differential equations sin cosy sin x + cos( y), has an equilibrium point at (0,T) (a) Calculate the Jacobian matrix of this system of equations and evaluate this matrix at the given equilibrium point. (b) Use your answer to part (a) to classify this equilibrium point.
The system of non-linear differential equations sin cosy sin x + cos( y), has an equilibrium point at (0,T) (a) Calculate the Jacobian matrix of this system of equations and...
Please show all work
Consider the following x'=(-7-28 (a) Find a fundamental matrix for the given system of equations. Ψ(t)-(-2e7t sin 14t Ψ(t) =(-2 sin 14t Ψ(t)-(2e-r sin 14t 2e-7 cos 14t e cos 1 esin 14t 2e-7r cos 14t cos 14t esin 14t O -2e-7 cos 14t e cos 1 esin 14t 2e sin 14t e7 e cos 14t2e sin 14t cos 14t Ψ(t)--2e7t sin 14t 2e"cos 14t e cos 14 sin 14t (b) Also find the fundamental matrix...
I. The state vector φ(t) at time t can be decomposed on the {I +), l-)} basis: Write down the system of coupled differential equations which the components c+ (t) and c() satisfy 2. Let |φ(1-0)) be decomposed on the {lx+), lx-) basis. Show that c+(1)-(Ηφ(t)) is written as sin with Ω 2VA2+B2. Here f.Ω is the energy difference of the two levels. Show that c+(1) (as well as c (t)) satisfies the differential equation c) 0. We assume that...
which one is right?
cost 2 + a. sin o cos o sint rect csct b. -2 tan^0 C. 1 + cott d. sint tant