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pik1432

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6 years, 123 days
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These are questions asked by pik1432

RE: incomplete substitution...

pik1432 245 Maple 2020
substitution
January 03 2021
3 3

Hello there, 

First of all, happy new year to you and those around you!

One question: would you teach me how to replace the 'Zs/Z_AB' expression in the last term of the expression 'eq_5_m5'?

In other words, I wanted to see the 'desired' expression, but the 'subs()' command repalced the first occurance of the 'Zs/Z_AB' expression. 

(Perhaps, this applet behind of this edit box does not like the Microsoft Edge browser)

Maple Worksheet - Error

Failed to load the worksheet /maplenet/convert/Q20210103.mw .
 

Download Q20210103.mw


Maple Worksheet - Error

Failed to load the worksheet /maplenet/convert/Q20210103.mw .

Download Q20210103.mw

 

Re: Further simplification...

pik1432 245 Maple 2020
radical simplification
December 08 2020
2 5

Hello there, 

Would you allow me to ask this question?

What would be a way to simplify the expression 'eq9_32a' below to the 'Desired' expression?

Intuitively, the numerator and denominator can be divided by 'sqrt(r^2 + 1)', but the 'Simplify' instruction did not do that. 
 

> 

restart;
> 

eq9_30 := T__e_n = 2*(s/s_hat) / ((1+r*s/s_hat)^2+(s/s_hat)^2);

T__e_n = 2*s/(s_hat*((1+r*s/s_hat)^2+s^2/s_hat^2))

 (1)
> 

eq9_31 := solve(diff(rhs(eq9_30), s)=0,s);

s_hat/(r^2+1)^(1/2), -s_hat/(r^2+1)^(1/2)

 (2)
> 

eq9_32a :=  T__e_np = simplify(subs(s=eq9_31[1] , rhs(eq9_30))) assuming r::real;

T__e_np = (r^2+1)^(1/2)/(r^2+(r^2+1)^(1/2)*r+1)

 (3)
> 

Desired := T__e_np = 1/(sqrt(r^2 + 1) + r);

T__e_np = 1/((r^2+1)^(1/2)+r)

 (4)
> 

 


Merry Christmas!

Download Q20201208.mw

RE: substitution...

pik1432 245 Maple 2020
substitution
December 04 2020
2 3

Hello there, 

Would you please tell me how to make the expression 'eq9_13_m3' into 'desired' by substituting part of 'eq9_13_m3' with 'aux2' expression?


 

> 

restart;
> 

eq9_13_m3 := 2*R__R*s*omega__s*L__sigma_S/(s^2*L__sigma_S^2*omega__s^2 + R__R^2);

2*R__R*s*omega__s*L__sigma_S/(s^2*L__sigma_S^2*omega__s^2+R__R^2)

 (1)
> 

aux2 := s_hat = R__R/(L__sigma_S*omega__s*s);

s_hat = R__R/(omega__s*L__sigma_S*s)

 (2)
> 

desired := 2*(s/s_hat) / (1+(s/s_hat)^2);

2*s/(s_hat*(1+s^2/s_hat^2))

 (3)
> 

 


Merry Christmas!

Download Q20201204.mw

How to cancel I and exp(-pi/2)...

pik1432 245 Maple 2020
syntax pi simplification
November 18 2020
3 5

Hello there, 

Would you allow me to ask this question?

What would be a way to make the 'expression' as 'expression_desired' below?

In other words, what would be a way to cancel I (or j) and exp(-pi/2) each other?


 

> 

restart;
> 

expression := exp(-I/2*(-2*rho__m + pi))*I;

I*exp(-((1/2)*I)*(-2*rho__m+pi))

 (1)
> 

expression_desired := exp(I*(rho__m));
> 

 

exp(I*rho__m)

 (2)
> 

 


Thank you, 

Download Q20201118.mw

RE: How to check if two expressions are ...

pik1432 245 Maple 2019
simplification arctan
November 09 2020
2 3

Hello there, 

Would you tell me how to check if the two expressions presented below are the same?

My simple attempt (at the end of the worksheet below) failed. 

This page might be helpful to check the equality: https://www.myphysicslab.com/springs/trig-identity-en.html
 

> 

restart;
> 

subexpx := Ls*cos(omega*t + phi__l + theta)*omega + sin(omega*t + phi__l + theta)*Rs;

Ls*cos(omega*t+phi__l+theta)*omega+sin(omega*t+phi__l+theta)*Rs

 (1)
> 

subexpx2 := sqrt((omega*Ls)^2+Rs^2)*sin(omega*t + phi__l + theta + arctan(omega*Ls/Rs));

(Ls^2*omega^2+Rs^2)^(1/2)*sin(omega*t+phi__l+theta+arctan(omega*Ls/Rs))

 (2)
> 

is(subexpx - subexpx2 = 0) assuming omega::positive, Ls::positive, Rs::positive;

false

 (3)
> 

 

> 

 


Thank you,

Download Q20201108.mw

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