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    Linearising compound pendulum equation

    That's because I thought I was allowed to measure the pendulums mass. Don't worry I've worked it out...finally, turns out I've been overcomplicating things. I'll just plot a graph of h^2 against h*T^2 the y intercept will be -k^2 and the gradient will be g/4pi^2. Thanks anyway.
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    Linearising compound pendulum equation

    hmmm, my only issue is that its the sqrt of K^2 + h^2 divided by gh it also turns out that k is the radius of gyration and I have no scales to measure the pendulum's mass. I believe I need a y=mx + c where the y intercept will be determined by k, g by m, x by T and h by y. is there any way...
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    Linearising compound pendulum equation

    I would have to make the axis √((h^2 + K^2)/gh ) but that is a good point. However, I would still like to know how I could linearise it further. I know that a taylor approximation is needed but I don't know how to, or what a value to choose
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    Linearising compound pendulum equation

    Homework Statement Linearise T=2pi√(K^2 + h^2)/gh K is known constant This is a compound pendulum equation, I want to plot some kind of formula with variable T against some kind of formula with variable H in order to find g from the gradient. Homework Equations The Attempt at a...
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    Angular acceleration problem

    Yes, that was my problem all along... I forgot to add the constant!! Thanks.
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    Angular acceleration problem

    Someone please help me!!!!
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    Angular acceleration problem

    But then I end up with t=1/2w, how do I find the rest of the answer?
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    Angular acceleration problem

    Homework Statement angular acceleration of line a= -2w^2 rad/s when theta=pi/6, w= 10 rad/s what is angular velocity when theta= pi/3? Homework Equations chain rule The Attempt at a Solution w= e^-2theta is my answer, but I know this is wrong I know that this question is...
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    Series expansion of logarithmic function ln(cosx)

    thanks, i'm not entirely certain, but is the differential -tanx?
  10. S

    Series expansion of logarithmic function

    How do I find the first three non-zero terms of ln(5+p), I'm pretty sure that my answer is wrong.
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    Series expansion of logarithmic function ln(cosx)

    okay, so It's wrong... where exactly have I messed up then?
  12. S

    Power series in real world situation

    Homework Statement A heavy weight is suspended by a cable and pulled to one side by a force F. How much force is required to hold the weight in equilibrium at a given distance x to one side. Tcosθ=W and Tsinθ=F. Find F/W as a power series of θ. Often in a problem like this, what we know is not...
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    Series expansion of logarithmic function

    Come on guys! I really need to know how to do this!
  14. S

    Power series when variable is very large

    Homework Statement Find first three non zero terms in series expansion for ln(1+e^-z) when z is very large Homework Equations The Attempt at a Solution I've got as far as ln(1+e^(-1/z)*e^((1/z)(z^(2) - 1)) not sure where to go from here
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    Series expansion of logarithmic function ln(cosx)

    Homework Statement A question asks me to find the first three non-zero terms of ln(cosx) Homework Equations The Attempt at a Solution I wrote cos x as 1+(1-cos x), used the power series of ln function, expanded cosx and simplified, here is my answer: 1/2x^2 - 1/6x^4 + 1/16x^6...
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    Series expansion of logarithmic function

    Homework Statement Find first three non zero terms in series expansion where the argument of funstion is small ln(5+p) Homework Equations The Attempt at a Solution The only way I could think how to do this is by saying ln(5+p) = ln(1+(4+p)) and expanding to (4+p)-...
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    Proof of inverse trigonometric identities

    Homework Statement Show that arcsin(1/sqrt(5)) + arcsine(2/sqrt(5)) = Pi/2 Homework Equations The Attempt at a Solution Can someone please give me so much as a hint?
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    Roots of cubic equation

    Homework Statement θ^3 - pθ^2 +qθ - r = 0 such that p and r do not equal zero If the roots can be written in the form ak^-1, a, and ak for some constants a and k, show that one root is q/p and that q^3 - rp^3 = 0. Also, show that if r=q^3/p^3, show that q/p is a root and that the product...
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    Polynomial expression of Pendulum period with respect to angle (large)

    [b]1. Homework Statement The swinging period T(θ) for a small amplitude simple pendulum, is given by T, a constant for a constant length pendulum. If the initial angle θ is large, then the amplitude becomes large and the period needs to be corrected. The correction to the large amplitude...
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    Power series question involving classical mechanics

    Homework Statement A heavy weight is suspended by a cable and pulled to one side by a force F. How much force is required to hold the weight in equilibrium at a given distance x to one side. From classical mechanics, TcosX= W and TsinX=F. Find F/W as a power series of X(angle). Often in a...
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    Binomial expansion of relativistic formula

    Homework Statement The speed v of electrons from a high energy accelerator is very near the speed of light c. Given the voltage V of the accelerator, calculate the ratio v/c. The relativistic formulafor this calculation is (see relevant equations) Use the binomial series to find (1-v/c) in...
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    Complex numbers in polar form

    Beacause the answer is apparently 2e^i((pi + 2kpi)/4) where K=0,1,2,3 that's why it wouldn't be right.
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    Complex numbers in polar form

    why are you wasting my time?
  24. S

    Complex numbers in polar form

    okay so you think the argument in pi
  25. S

    Complex numbers in polar form

    are you saying that the argument is zero and that the modulus is 16?
  26. S

    Complex numbers in polar form

    How do I draw -16 in the complex plane, when I don't know r or theta?
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