Recent content by Varnson

Sorry for that... I used the equation d^2u/dtheta^2 + u = (-1/ml^2u^2)*f(u^-1). For the second derivative of u with respect to theta i got 2*a*theta^-3, which i re-wrote as 2*a^2*u^3. I plugged that result into the diff. equation, but was unable to 'get rid of' the factor of 2 for the a^2...

Homework Statement A particle moves under the action of a central force in a spiral orbit given by r=a*theta. Show that the force is f(r) = (-L^2/mr^3)*[1 + (a^2)/(r^2)] Homework Equations The Attempt at a Solution I know how to do the problem, but I keep ending up with a...

I figured it out, thanks for the pointers!

[SOLVED] Mechnics - Small Oscillations Homework Statement A body of uniform cross-sectional are A= 1cm^2 and a mass of density p= 0.8g/cm^3floats in a liquid of density po=1g/cm^3 and at equilibrium displaces a volume of V=0.8cm^3. Show that the period of small oscillations about the...

I solved it, for some reason I just couldn't see it adn it was sitting in front of me lol. Thanks for the help!

Driven, damped oscillator - URGENT! Homework Statement A driven, undamped oscillator has an amplitude of 3.0cm at a driving frequency of 9 rad/s and an amplitude of 2.4cm at a driving frequency of 7 rad/s. What is the resonant frequency of the oscillator? Homework Equations A =...

Homework Statement A particle slides under gravity along a smooth path in the x-z plane by z=b-(x^2/a). Show that the energy of this motion can be expressed as E=.5m*xdot^2*[1+(2x/a)^2] + mgb[1-(x^2/ab)] Homework Equations T(A)+V(A) = T(B)+V(B), where T is kinetic energy The...

I was not able to get the diff. eq. I have not had any diff. eq. classes yet, so I am teaching myself as I go along in my mechanics course. Would it be ma=-mg-c1v?

Homework Statement A projectile with mass m is fired upward with an initial speed v0. If the air drag varies with the square of speed F(v)=-kmv2 show that the projectile reaches a height of h=1/2k*ln[1+(kv0^2/g)] Homework Equations F0+F(v) =...

Homework Statement Assume that a water droplet falling through a humid atmosphere gathers up mass at a rate that is proportional to its cross-sectional area A. Assumethat the droplet starts from rest and that its initial radius R0 is so small that it suffers no resistive force. Show that its...

I figured it out, I was stuck after I took the derivative, then i solved for r/d and the answer was right there in front of me! Thanks for the help!

Homework Statement A body follows an elliptical path defined by r = sd/(1-s*cosP), where s and d are constant. If the angular speed is constant (dP/dT = w), show that the body's speed is v = rw[1+{(r*sinP)/d}^2]^(1/2) Homework Equations v = dr/dT*rhat + r*dP/dT*Phat; P = theta, I am...

Also, if the line is moved a distance 'D' which is greater than 'R' would the force on it be zero? I am thinking no, because the force from the more top of the sphere is greater than the force on the bottom so they won't cancel out. I am assuming the same for the other two direction as well.

Am I correct if I choose two arbitrary points at each end of the line to figure out the dipole for the line?

That is what I was thinking. What vector would you choose for your source vector?