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...
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...
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...
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
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...
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)-...
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?
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...
[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...
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...
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...
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??
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...
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?
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...
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.