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Question: This is RLC series circuits current response when ...

Question:This is RLC series circuits current response when ...

Tokoro 115 Maple
dsolve differential-equations plotting inttrans
February 08 2022
1

L=100 H, R=20 ohm, C=1/401 F, DC=200 V and Impulse =2000 V. q(0)=0 and Q'(0)=2000/L.
Maple new user can't show the ODE function. I just use the toolber menu. 

Tokoro.

> 

restart;
with(inttrans):
U__0:=20:
> 

U := t -> U__0*exp(-1/10*t)*cos(2*t):
> 

plot(U(t), t = 0 .. 2*Pi,
     axis[2] = [tickmarks = [0 = 0, 20 = U__0]],
     labels = [t, 'U(t)'], size=[500,300]);

 
> 

laplace(U(t), t, s)

200*(10*s+1)/((10*s+1)^2+400)

 (1)
> 

simplify(200*(10*s+1)/((10*s+1)^2+400))

(2000*s+200)/(100*s^2+20*s+401)

 (2)
> 

expand((2000*s+200)/(100*s^2+20*s+401))

2000*s/(100*s^2+20*s+401)+200/(100*s^2+20*s+401)

 (3)
> 

"Y(s):=((20)/(s)*100*s)/(100 s+20+401/(s))+(200/(s))/(100 s+20+401/(s))"

proc (s) options operator, arrow, function_assign; 2000/(100*s+20+401/s)+200/(s*(100*s+20+401/s)) end proc

 (4)

" y(t):=invlaplace(Y(s),s,t):"

plot(y(t), t = 0 .. 2*Pi, axis[2] = [tickmarks = [0 = 0, 20 = U__0]], labels = [t, 'U(t)'], size = [500, 300])

  
> 

Parse:-ConvertTo1D, "first argument to _Inert_ASSIGN must be assignable"

Error, illegal use of an object as a name

"L:=100:R:=20:C:=1/401:E:=200:L*i(0):=2000:q(0):=0:"

  

NULL

> 

NULL
> 

dsolve[interactive]()
> 

 

Error, invalid function arguments

"diff(,t)"

  
> 

plot([diff(q(t), t), 20*exp(-(1/10)*t)*cos(2*t)], t = 0 .. 2*Pi)

Warning, expecting only range variable t in expression diff(q(t),t) to be plotted but found name q

  

 
> 

plot([q(t), (4000/401)*exp(-(1/10)*t)*sin(2*t)-(200/401)*exp(-(1/10)*t)*cos(2*t)+200/401], t = 0 .. 2*Pi)

Warning, expecting only range variable t in expression q(t) to be plotted but found name q

  

 
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