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The problem asks me to show that the addition of two cosines with different wavelength and frequencies gives a solution with beats. Mathematically, I need to verify that A cos (k1x-w1t)+A cos (k2x-w2t) is equivalent to A cos (.5(k1+k2)x-.5(w1+w2)t) cos (.5(k1-k2)x-.5(w1-w2)t) I converted...

I think that velocity to be v0, not zero. Otherwise, the problem is trivial. I just wanted to check and make sure I wasn't missing anything :smile:

It moves along the x-axis...I forgot to mention that. So gravity is not taken into consideration?

Question answered! Thanks for the input!

Thanks for being so prompt and helpful in your response! So, constrained to move in a circle...that sounds like polar coordinates! So the third term I am missing is the expression of kinetic energy for the disc in polar coordinates? So I should find the center of mass of the disk, and that...

Thanks so much for the help...but I need some further clarification. You said that the contribution to KE comes from the fact that the disk's center of mass can move. How do I express this mathematically as a term in my kinetic energy expression? Is what I have for Kinetic energy thus far...

Lagrange Problem redux -- super urgent... See the attachment to help you visualize this. A rod of length L and mass m is povoted at the origin and swings in the vertical plane. The other end of the rod is attached/pivoted to the center of a thin disk of mass m and radius r. OK, I know that...

We have a rod of length L and mass M pivoted at a point at the origin. This rod can swing in the vertical plane. The other end of the rod is pivoted to the center of a thin disk of mass M and radius R. Derive the equations of motion for the system. I have attached a drawing :) If you...

The system examined in the problem is depicted below: ^^^^^(m1)^^^^^(m2) m1 and m2 are connected by a spring and m1 is connected to the wall by a spring. The spring constant is k. T = m/2 [ x1'^2 +x2'^2 ] kinetic energy of system (x1' is velocity of m1, x2' is velocity of m2) U = 1/2 m...

The problem I am working on asks me to find the curve on the surface z=x^(3/2) which minimizes arc length and connects the points (0,0,0) and (1,1,1). Here's what I did: Integral [sqrt(dx^2+dy^2+dz^2)] Integral [dx sqrt (1+(dy/dx)^2 +(dz/dx)^2] Integral [dx sqrt (1 + (dy/dx)^2 + 9x/4)]...

Lagrangian Dynamics problem -- need help with setup Here's the problem: A simple pendulum of length b and bob with mass m is attached to a massless support moving horizontally with constant acceleration a. Determine the equations of motion. For the pendulum, x = b sin theta and y = b cos...

Two masses connected by a single spring m1 --------m2 I hope this helps to make the geometry clear. I need help with this urgently :)

Two masses m1=100g and m2=200g slide freely in a horizontal frictionless track and are connected by a spring whoser force constant is k=.5 N/m. Find the frequency of oscillatory motion for this system. Could someone give me a hint/help me get started on this? What equation(s) should I...

Thanks for the input!