Homework Statement
Consider the Atwood’s pulley shown below. The masses are 4m, 3m, and m. Let x and y be the directed distances from the centers of the fixed (i.e. inertial) top pulleys for the left and right masses as indicated.
http://imgur.com/VXEygxt
a) Write down the Lagrangian...
Homework Statement
I'm having problems with some differential equations, just need to know where I'm going wrong.
Homework Equations
The Attempt at a Solution
a) mv\stackrel{dv}{dx}=F(x)
mvdv=F(x)dx
m∫vdv=∫F(x)dx
v^2=vv^{2}_{0}+\stackrel{2}{m}∫F(x)dx...
Homework Statement
Solve the initial value problem:
t(dy/dt)+8y=t^3 where t>0 and y(1)=0
Homework Equations
None?
The Attempt at a Solution
It's a linear equation, so rearranged to dy/dt+8y/t=t^2.
Took the integrating factor e^(∫8/tdt)=t^8 and multiplied through...
Homework Statement
Find the radius and the interval of convergence for the series:
Ʃ((-1)nxn)/(4nlnn) with sum n=2 to ∞.
Homework Equations
The Attempt at a Solution
I'm testing for the left and right side of the interval. I've found that cn=1/(lnn), an=1/4, and R=1. I used...
Homework Statement
Ʃan (sum from n=1 to ∞) converges.
1) Determine whether the series Ʃln(1+an) (sum from n=1 to ∞) converges or diverges. Assume that an>0 for all n.
2) Show each of the following statements or give a counter-example that establishes that it is false:
a)Ʃai2 (sum i=1...
Homework Statement
\sum(\frac{2n}{2n+1})n2
(The sum being from n=1 to ∞).
Homework Equations
The Attempt at a Solution
Used exponent properties to get (\frac{2n}{2n+1})2n. Using the root test, the nth root of an = lim n->∞(\frac{2n}{2n+1})2 = 1. However, the root test is...