# Search results

1. ### 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...
2. ### 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...
3. ### 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...
4. ### 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
5. ### 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...
6. ### 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)-...
7. ### 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?
8. ### 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...
9. ### 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...
10. ### 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...
11. ### 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...
12. ### Complex numbers in polar form

Homework Statement Compute the 4th roots of -16 in both Cartesian and polar form and plot their positions in the complex plane. Homework Equations z^1/n=(r^1/n)(e^i(theta)/n), (r^1/n)(e^i(theta)/n)(e^i2(pi)/n........ The Attempt at a Solution How do I find the value of r, and theta??
13. ### Complex numbers in polar form

Homework Statement Evaluate the square 0f 5e^(3(pi)i)/4 without using Cartesian form, and also the three different products. Homework Equations e^i(theta) = cos(theta) + isin(theta)? The Attempt at a Solution I have absolutely no idea here, nothing in my notes even begins to...
14. ### Maths project

Maths project proving lim n-infinity (1+x/n)^n = exp(x) Homework Statement project aiming to show that limn→∞(1+x/n)^n = exp(x) Homework Equations The Attempt at a Solution I have no Idea, is there any chance someone could give me some sort of clue?
15. ### Geometric sequences

Homework Statement A mortgage is taken out for £80,000. It is to be paid by annual instalments of 5000with the first payment being made at the end of the first year that the mortgage was taken out. Interest of 4% is then charged on any outstanding debt. Find the total time taken to pay off the...
16. ### Sin cosine rule

soine cosine rule I have a question for you, I came across this question while revising for my exam on monday if anyone can answer this I'll be very impressed. Two different trangles ABC have AB=5cm, AC=3.2cm and angle ABC=35degrees calculate the difference between their areas.