Recent content by derravaragh

Homework Statement Apply saddle point approximation to the following integral: I = ∫0∞xe-ax-b/√xdx a,b > 0 Recall that to derive Stirling formula from the Euler integral in class we required N >> 1. For the integral defined above, identify in terms of a and b appropriate parameter that...

Homework Statement The wave function for a particle of mass m moving in the potential V = { ∞ for x=0 { 0 for 0 < x ≤ a { V0 for x ≥ a is ψ(x) { Asin(kx) for 0 < x ≤ a { Ce-Kx for x ≥ a with k = √[(2mE/h2)] K =√[((2m(V0-E)/h2)] where h is h-bar in both equations, and...

Homework Statement Three identical small balls of mass m with uniformly distributed charge Q each hang from a string of length L. The strings are all tethered at the opposite end at the same point. (a) Find the general equation for the angle θ of each string from vertical. Homework...

Ok, I'm confused here. I'm continuing forward with L = mvr(ψ)sin(θ), but I don't understand why I don't need to get v, since v isn't constant? I know that when taking the time derivative of L one of the terms is r x p = 0 because they parallel

Ok, well my intuition tells me to make L=r(psi)mvsin(θ) where θ is the angle between the positive x-axis and the line from the focal point to the point in the orbit In my notes, we proved momentum was constant by making momentum L = m(x*vy - y*vx) and converting to polar coordinates. Does this...

Homework Statement The figure illustrates a Keplerian orbit, with Cartesian coordinates (x,y) and plane polar coordinates (r,φ). F = -(G*M*m)/r^2 The parametric equations for the orbit: r(ψ) = a ( 1 − e cos ψ) tan(φ/2) = [(1+e)/(1-e)]^(1/2)* tan(ψ/2) t(ψ) = (T/2π) ( ψ − e sin ψ) where ψ is the...

Homework Statement Assume that the interior of the Earth is an incompressible fluid. The density is constant: ρ = M/V. The pressure p(r) depends on the distance r from the center of the earth. The equation for static equilibrium of a self-gravitating fluid sphere is p(r)δA − p(r+dr)δA −...

Ok, that makes sense. Thank you for the help.

Homework Statement (A) A damped oscillator is described by the equation m x′′ = −b x′− kx . What is the condition for critical damping? Assume this condition is satisfied. (B) For t < 0 the mass is at rest at x = 0. The mass is set in motion by a sharp impulsive force at t = 0, so...

I just realized I gave the wrong set of equations, that one doesn't match the other three I got, but it's the same concept. I see my issue now, pretty simple. Thank you for your help.

Homework Statement Consider a 2-D elastic collision between two masses. The first mass is moving at initial speed v0 towards the second mass. The second mass is initially at rest. Mass m1 = 0.1 kg and mass m2 = 0.2 kg. The first mass recoils at 30° above the horizontal at speed v1, and the...

Homework Statement (a) Consider a binary star system in which the two stars have masses M1 and M2 and the stars move on circular orbits separated by a distance R. Derive the formula for the period of revolution. (b) Suppose M1= 1.22M and M2= 0.64M (where M = mass of the sun) and R= 0.63...

I realized where I went wrong, I had solved for the time t when the entire chain had fallen over the side, so I went back and solved for when x(t) = L/2. Thank you for your help.

Homework Statement A flexible chain of mass M and length L lies on a frictionless table, with a very short portion of its length L0 hanging through a hole. Initially the chain is at rest. Find a general equation for y(t), the length of chain through the hole, as a function of time. (Hint: Use...

For the first response, I rechecked my work on part (a) and realized my signs were off, using A = b the ∫Ae^(-bt) from 0 to ∞ gives me a value of +1. For the second response, the only solution I can think of would be the Expected value E(x) which would give E(t) = ƩtP(t) = Ʃt(Ae^(-bt)) from t...