Sketch curves of x-1 versus T for T > Tc for (a) a paramagnet, (b) a...
2) Sketch the phase portrait of the system x' (t) = Ax (t) if (a) 5= [ 9), P=[7"}] (1) 5= [ • ? ], P=[} >>]
A= 10 5 5 2 B= 4. 1 > ,A+B= . ] 0
(b) If R = 4solve and sketch the response of voltage, V(t) when t > 0. Next, obtain the current I flowing through the inductor in Figure Q3(b). [16 marks) t = 0 422 IH wm + + 24 V 0.25 F V(t) R Figure Q3(b)
1. (a) Suppose the unit step function uc(t) has a generalized derivative u(t) everywhere. Find L[u'(t)] for c > 0. What generalized function is u(t) equal to do you think?
4. Rank the following types of electromagnetic radiation in order of decreasing energy. X-rays > Ultraviolet > Visible > Microwaves b) Microwaves > Visible > Ultraviolet > X-rays c) Microwaves > Ultraviolet > Visible > X-rays d) X-rays > Visible > Ultraviolet > Microwaves 24. Which of the following arrangements is in order of increasing size? a) Ca2+> K+ > C1-> S2- b) Ca2+ <K+ < Cl< S2- c) 52-> Cl- > Ca2+> K+ d) $2- < Cl- <K+ <...
Could someone explain how these to get these phase portraits by hand with ẋ=y and ẏ=ax-x^2 especially for a=0 case where you have eigenvalues all equal to zero? 6.5.4 a>0 Sketch the phase portrait for the system x = ax-x, for a < 0, a = 0, and For a -(0 We were unable to transcribe this imageFor a>0 ES CS
x" dx TC 15. (a) So 1 + x x for 0 < a < 1. sin πα
Consider the linear system of first order differential equations x' = Ax, where x = x(t), t > 0, and A has the eigenvalues and eigenvectors below. Sketch the phase portrait. Please label your axes. 11 = 5, V1 = 12 = 2, V2 = ()
3. Let T = {< M > | m accepts w" when it accepts w. }. Show T is undecidable.
Please include step-by-step solution. D19. Solve t2x" +3tx -3 x-t', t>0.