Tokoro

115 Reputation

5 Badges

2 years, 209 days

MaplePrimes Activity


These are replies submitted by Tokoro

@Tokoro The answer of 7 points. 

@Tokoro T. Suzuki find the minimum radius answers for points untill 24.

@Tokoro  This is new answer for 5 points. And this is the minimum r for 5 points. T. Suzuki find this answer.

Thanks Kitonum 19099 and sursumCorda 20.

Both methods solve this puzzle symbolically. 

Tokoro.


 

:RLC circuit I want to solve.

restart

with(DynamicSystems); with(inttrans)

E := 1; J := 3; R := 3; L := 1; C := 1/2

(1/s-6/s^2)/(s+3+2/s)

(1/s-6/s^2)/(s+3+2/s)

(1)

i__RL := proc (t) options operator, arrow; invlaplace((1/s-6/s^2)/(s+3+2/s), s, t) end proc

proc (t) options operator, arrow; invlaplace((1/s-6/s^2)/(s+3+2/s), s, t) end proc

(2)

"(->)"

-4*exp(-2*t)-3+7*exp(-t)

(3)

e__C := proc (t) options operator, arrow; E-i__RL(t)*R-L*(diff(i__RL(t), t)) end proc

proc (t) options operator, arrow; E-i__RL(t)*R-L*(diff(i__RL(t), t)) end proc

(4)

"(->)"

10+4*exp(-2*t)-14*exp(-t)

(5)

plot([-4*exp(-2*t)-3+7*exp(-t), 10+4*exp(-2*t)-14*exp(-t)], t = 0 .. 10, color = [red, blue], thickness = 3, labels = ["t", "i(t)_red and vc(t)_blue"])

 

NULL

(1/s-6/s^2)/(s+3+2/s)

(1/s-6/s^2)/(s+3+2/s)

(6)

Solve eq(6) by Maple's dsolve.

E := 1; R := 3; C := 1/2; L := 1; J := 3

sol := dsolve([L*(diff(diff(q(t), t), t))+R*(diff(q(t), t))+q(t)/C = 1-6*t, q(0) = 0, (D(q))(0) = 0])

q(t) = 2*exp(-2*t)-7*exp(-t)-3*t+5

(7)

rhs(q(t) = 2*exp(-2*t)-7*exp(-t)-3*t+5)

2*exp(-2*t)-7*exp(-t)-3*t+5

(8)

plot(diff(2*exp(-2*t)-7*exp(-t)-3*t+5, t), t = 0 .. 10, color = red, thickness = 3)

 

v[c] := proc (t) options operator, arrow; E-R*(diff(2*exp(-2*t)-7*exp(-t)-3*t+5, t))-L*(diff(2*exp(-2*t)-7*exp(-t)-3*t+5, t, t)) end proc

proc (t) options operator, arrow; E-R*(diff(2*exp(-2*t)-7*exp(-t)-3*t+5, t))-L*(diff(2*exp(-2*t)-7*exp(-t)-3*t+5, t, t)) end proc

(9)

(proc (t) options operator, arrow; E-R*(diff(2*exp(-2*t)-7*exp(-t)-3*t+5, t))-L*(diff(2*exp(-2*t)-7*exp(-t)-3*t+5, t, t)) end proc)(t)

10+4*exp(-2*t)-14*exp(-t)

(10)

i__c := proc (t) options operator, arrow; diff(C*(10+4*exp(-2*t)-14*exp(-t)), t) end proc

proc (t) options operator, arrow; diff(C*(10+4*exp(-2*t)-14*exp(-t)), t) end proc

(11)

(proc (t) options operator, arrow; diff(C*(10+4*exp(-2*t)-14*exp(-t)), t) end proc)(t)

-4*exp(-2*t)+7*exp(-t)

(12)

plot([10+4*exp(-2*t)-14*exp(-t), -4*exp(-2*t)+7*exp(-t)], t = 0 .. 5, color = ["red", "blue"], thickness = 3, labels = ["t", "vc(t)_red,ic(t)_blue"])

 

NULL

NULL


 

Download DynamicSystem-How_to_ODE.mw

@Preben Alsholm It makes equation (7). And I want to solve this ODE in Eq.(7) by Maple.

Using laplace convertion, I can get the answer and can plot it.

@acer Thanks show me the power of Maple. 

@acer Thanks your follow up. I try to find the mimimum of the intersect. 

Optimization can find it. How to find by min(extrema....? 

 

Totoro.

plot-15-iPlot.mw 

@tomleslie x=45, y=45, intersect=2.117 may be the maximum of intersect. How to find this value by Maple?