Ok so i have a homework problem again :) This time it's a simple pendulum swing and the question is as follows:(adsbygoogle = window.adsbygoogle || []).push({});

"Prove that the tension in the string of a simple pendulum when the string makes an angle [tex]\theta[/tex] with the vertical is approximately [tex]mg(1 + \theta^2_0 - (3/2)\theta^2[/tex] where m is the mass of the bob and [tex]\theta_0[/tex] is the value of [tex]\theta[/tex] at the extremes of the motion."

Now our teacher gave us a bit of help, saying that we should use a taylor polynom to solve this, as well as the formula:

[tex]x(t) = x_0 * cos(\omega * t)[/tex]

Where [tex]x_0[/tex] is x (or s if you prefer) at the extremes of it's motion.

So i basicly want to find the formula for the total force on the string right? So i got the resultating forces:

[tex]F_{res} = mg*cos(\theta) + F_{string} = ma = m(v^2/r)[/tex]

And hence i isolate the force on the string

[tex]m(v^2/r) - mg*cos(\theta) = F_{string}[/tex]

I'm not entirely sure what to do next. I'm not sure if i should be making the Taylor Polynom out of

[tex]x(t) = x_0 * cos(\omega * t)[/tex]

Can i simplify that down to only cos(theta) ? That would be easy enough and could perhaps get that to fit the formula given in the question (i'm thinking maybe if i could do that i could replace v^2 in the above example with 2Ax and use the taylor polynom insted of x in the point theta_0 and then substitute cos(theta) with the taylor polynom of theta). Someone also tried to hint to me i should use the preservation of energy, but i'm not seeing where that should enter the picture.

If someone could perhaps nudge me in the right direction that would be great (now i just gotta hope all that latex came through as intended).

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# Homework Help: Problem proving tension in string

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