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    Verifying A Cosines Addition Equation with Beats

    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...
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    Newton's Second Law

    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:
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    Newton's Second Law

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

    Question answered! Thanks for the input!
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    Lagrange Problem redux - super

    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...
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    Lagrange Problem redux - super

    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...
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    Lagrange Problem redux - super

    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...
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    LaGrange problem

    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...
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    Lagrangian for system with springs

    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...
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    Minimizing arc length

    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)]...
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    Lagrangian Dynamics problem - with setup

    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...
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    Harmonic Motion Problem

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

    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...
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    Atwood's machine problem - inclined plane

    Thanks for the input!