Recent content by physics148

Homework Statement Okay, so the question I'm trying to solve is to find the quantized energies for a particle in the potential: $$V(x)=V_0 \left ( \frac{b}{x}-\frac{x}{b} \right )^2$$ for some constant b. The Attempt at a Solution I am following along with the derivation of the quantized...

Homework Statement A particle of mass m1 collides with a particle of mass m2 initially moving at right angles to it(see Figure 1 below). Calculate the final velocities of each particle, and the angles at which the particles leave the collision site( as measured with respect to the original...

awesome. figured it out by taking the limit. thanks!

Homework Statement (2) Suppose a particle of mass m is subjected to a repulsive force F = +kx. (a) What is the general solution for the motion of the system? (b) If the particle begins with a position x(0) = x0 and with velocity v(0) = v0 at t = 0 what are the values of the constants appearing...

Thank you, I fixed my errors and everything worked out

Sorry, our ##k## should be ##3k_1##, not ##-2k_1##. That would give us a real number for the frequency, but I'm still not sure if it makes sense based on the derivation for the angular frequency that we did in class

Sorry, I got the inside of of roots mixed up. Based on the taylor series expansion, we get ##F(x_0) = -k(x-x_0)##, where ##k=-F(x_0)##. Then for an initial point ##x_0=(\frac{k_2}{k_1})^{\frac 13}## ##k=-(k_1+\frac{k_2}{x^3})=-(k_1+k_2\frac{k_2}{(\frac{k_2}{k_1}^3)^{\frac 13}}=-2k_1##. The...

So, we solved for k, and got it to be equal to ##2k_1##. So the corresponding period then would just be ##2 \pi \sqrt{\frac{2k_1}{m}}## and the frequency is just ##\frac{1}{2\pi}\sqrt{\frac{m}{2k_1}}##?

Okay, thanks. Here is what we have so far, but we are getting stuck when trying to solve for the frequency, since we get it as an implicit function? For reference, our local min ##x_0=(\frac{k_2}{k_1})^{\frac13}##

I was thinking of using a taylor series expansion, but I'm unsure on how I would go about doing this? I"m not very proficient with taylor series, could you help me set it up?

Yup that's what I said for a and b. Not sure how F=-V' will help for part c? What formula do I use, and how do I use the fact that the amplitude is extremely small? Thanks

Homework Statement A potential energy function for a particle moving in one-dimension is given as: V (x) =k1x^2/(2)+k2/x (a) Locate all the equilibrium points. (b) Show that the motion is always periodic for any amount of total energy. (c) What is the frequency f the motion if the amplitude of...

Homework Statement While carrying contact lenses of D=-2.00 diopters, a nearsighted person takes a vision test and finds that his/her far point is 10.0m a) what is the person's far point without contact lenses? b) what lens power is required to correct the myopia fully? Homework Equations 1/f...