Mass of a wire in shape of helix

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Dinneharan Ravi Chamdran
Dinneharan Ravi Chamdran on 14 Jun 2022
Answered: Bjorn Gustavsson on 14 Jun 2022
syms x y z r t rho
x=cos(t*pi)
y=sin(t*pi)
z=8*t
r=[x,y,z]
rho=x^2+y^2+z^2
int(rho*norm(diff(r,t)),t,[0,1])
cos^2(x)+sin^2(x) should be equal to 1. As the problem above it not simply to 1. What are the way to simplify the answer by cos^2(pi*t)+sin^2(pi*t)= 1.
  1 Comment
Ganesh
Ganesh on 14 Jun 2022
Have you tried out the Simplify function?

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Answers (1)

Bjorn Gustavsson
Bjorn Gustavsson on 14 Jun 2022
The symbolic tools make the default interpretation that all variables are complex. Therefore it cannot make that simplification.
If you explicitly constrain the variables to be real and use the simplify suggestion by@Ganesh you get:
syms x y z r t rho real
x=cos(t*pi)
y=sin(t*pi)
z=8*t
r=[x,y,z]
rho=x^2+y^2+z^2
Lengthofhelix = simplify(int(rho*norm(diff(r,t)),t,[0,1]))
HTH

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