Small oscillations Definition and 63 Threads

Homework Statement Consider a particle of mass m constrained to move on the surface of a paraboloid whose equation (in cylindrical coordinates) is r^2=4az. If the particle is subject to a gravitational force, show that the frequency of small oscillations about a cirrcular orbit with radius...

[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...

Homework Statement a rope is tied between 2 walls as shown.a bead of mass 'm' is on the rope as shown. it is constrained to move in the horizontal direction. it is tied to a spring of force constant 'k'- N/m. the spring is initially at its free length 'H'. the bead is displaced by a small...

Does anyone know where I can get some information on how you can relate the frequency of small oscillations to the second derivative of potential energy. I saw this done recently in a qualifying exam level problem but I do not remember learning this method and it is not in my classical dynamics...

Homework Statement A coin of radius R is pivoted at a point that is distance d from the center. The coin is free to swing back and forth in the vertical plane defined by the plane of the coin. For what value of d is the frequency of small oscillations largest? Homework Equations...

A marble of radius b rolls back and forth in a shallow spherical dish of radius R. Find the frequency of small oscillations. You can solve this problem using conservation of energy or using Newton’s second law. Solve it both ways and show that you get the same answer. I kind of get the...

Estimate the spring constant in units of eV/A^2 for the hydrogen (H2) molecule from the potential energy curve shown below, where r is the distance between protons. From the spring constant and the reduced mass m=1/2m(proton), compute the vibrational frequency. This frequency corresponds to...

Hi see the attached picture... 2 coupled masses, each suspended from spring in gravitational field... also entire construction can vibrate only vertically... I need to write lagrangian for this system in the following form...

Hello, I solved the problem of small oscillations for a 3-atom molecule, such as CO2, which is modeled as 3 masses connected by 2 springs. Both springs have a constant k, the outer masses are m and the middle one is M. There are 3 modes of oscillations, and one of them is of course \omega...

I've been busy finishing my online physics homework, and I cannot get this problem for the life of me (which is annoying because I just finished the relativity and lorentz transformation assignments). If you are good at physics and think you know how to do it, please post your line of thoughts...

Hi, A particle is subjected to a central potential of: V(r) = -k\frac{e^{-\alpha r}}{r} Where k, \alpha are known, positive constants. If we make this problem one-dimensional, the effective potential of the particle is given by: V_{eff}(r) = -k\frac{e^{-\alpha r}}{r} + \frac{l^2}{2 m...

For small oscillations, the oscillation behaves like a spring, because the potential energy function can be approximated by a parabola at the equilibrium point. Now, the effective spring constant in these situations is equal to the second derivative of the potential energy function, and so the...

What is the frequency of SMALL oscillations about è[t] = 0 of the following expression: Assume that w t is a constant. A Cos[w t - è[t]] + B è''[t]==0, where A and B are arbitrary constants? If you expand the Cosine term, you get A Cos[w t] Cos[è[t]] + A Sin[w t] Sin[è[t]] +B è''[t] ==0...