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He said, “No!”.

Author zkchongPosted on February 9, 2013Categories ShareLeave a comment on He said, “No!”.

Merry Christmas!!

Author zkchongPosted on December 18, 2012November 15, 2013Format GalleryCategories ShareLeave a comment on Merry Christmas!!

Solving Math’s Assignment with Sage

Someone sent me this question:

“Solve for the currents in the circult of Figure 2, if E(t)=5H(t-2) and the initial currents are zero. [Hint : Use Lapalce transform to solve this problem.]”

So, to solve it, form mesh analysis of two loops. Then, convert them from time domain to complex domain with Laplace transform. Next, solve I1 and I2 with normal algebra. Then only inverse I1 and I2 back to time domain.

Of cause, if you familiar with Sage, you can solve it within 30min (or lesser?).

t = var('t')
s = var('s')
I1 = var('I1')
I2 = var('I2')

E(t) = 5*unit_step(t-2)

E(s) = E(t).laplace(t, s); E(s)
# >> 5*e^(-2*s)/s

equation = [
	-E(s) + I1*20*s + 10*(I1-I2) == 0,
	10*(I2-I1) + I2*30*s + I2*10 == 0 ]

solution = solve(equation, I1, I2); solution
# >> [[I1 == 1/2*(3*s + 2)*e^(-2*s)/(6*s^3 + 7*s^2 + s), I2 == 1/2*e^(-2*s)/(6*s^3 + 7*s^2 + s)]]

# Note that Sage cannot inverse-Laplace time-delay function. So, taking out e^(-2*s)
I1(s) = 1/2*(3*s + 2)/(6*s^3 + 7*s^2 + s)
I2(s) = 1/2/(6*s^3 + 7*s^2 + s)

i1_temp(t) = I1(s).inverse_laplace(s, t); i1_temp
# >>t |--> -1/10*e^(-t) - 9/10*e^(-1/6*t) + 1

i2_temp(t) = I2(s).inverse_laplace(s, t); i2_temp
# >> t |--> 1/10*e^(-t) - 3/5*e^(-1/6*t) + 1/2

# Referring to Table. For G(s)= e^(as)F(s), the inverse is g(t) = f(t-a).
u(t) = unit_step(t)
i1(t) = u(t-2) * ( -1/10*e^(-(t-2)) - 9/10*e^(-1/6*(t-2)) + 1 ) # Answer for i1
i2(t) = u(t-2) * ( 1/10*e^(-(t-2)) - 3/5*e^(-1/6*(t-2)) + 1/2 ) # Answer for i2

p1 = plot(i1(t), 0, 10, color='blue', legend_label='i1(t)')
p2 = plot(i2(t), 0, 10, color='red', legend_label='i2(t)')
show(p1 + p2)

And, the final answers are:

$i_1(t) =u(t)\left( \frac{-1}{10}e^{-(t-2)} -\frac{9}{10}e^{-(t-2)/6} +1 \right)$
$i_2(t) =u(t)\left( \frac{1}{10}e^{-(t-2)} -\frac{3}{5}e^{-(t-2)/6} +\frac{1}{2} \right)$

Author zkchongPosted on September 8, 2012September 8, 2012Categories ShareLeave a comment on Solving Math’s Assignment with Sage

Unboxing MBP

Unboxing Mac Book Poor, Ops. Sorry. I mean unboxing Mac Book Pro. ^^

Someone gonna be poor for the next 12 months.

Continue reading “Unboxing MBP”

Author zkchongPosted on August 25, 2012August 25, 2012Categories Share1 Comment on Unboxing MBP

Bye SAINT2012

I happened to be the last batch of speakers in SAINT2012 conference. Next year it will be merged with COMPSAC as “New COMPSAC”, which will be held in Kyoto in 2013. The name of “SAINT” will not be used anymore.

Speaker SAINT2012 — Badge in COMPSAC/SAINT2012

Happened to know that I have to teeeaaaach in the coming short-semester. It seems like I am getting far far away from my PhD completion. I blame noone but myself. When will I have the gut to tender resignation letter? When will I have the time to do nothing but my own research?