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    ODE question: Understanding a step in the solution

    Homework Statement Hi there, I don't nee help with solving a question, so much as understanding a step in the provided worked solution. It's using variation of parameters to solve the ode y''+ y = g(t). I've attached the steps in the picture file, and the bit after the word 'Now' what are they...
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    Variation of Parameters to solve a second order ODE

    Yes I had, thank you. I'll have another try!
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    Variation of Parameters to solve a second order ODE

    Homework Statement The question I am working on is the one in the file attached. Homework Equations y = u1y1 + u2y2 : u1'y1 + u2'y2 = 0 u1'y1' + u2'y2' = g(t) The Attempt at a Solution I think I have got part (i) completed, with y1 = e3it and y2 = e-3it. This gives a general solution to the...
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    Solving a second order ODE using reduction of order

    Homework Statement Hi there, I have an assignment which involves using reduction of order to solve for a second solution to an ode (the one attached). However this is a method I am new to, and though I have tried several times, I'm somehow getting something wrong because the LHS and RHS are not...
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    Mathematical Analysis Proof: |x-y|<= |x|+|y|

    Thank you all for your replies :)
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    Mathematical Analysis Proof: |x-y|<= |x|+|y|

    Homework Statement 1. Show that for all real numbers x and y: a) |x-y| ≤ |x| + |y| Homework Equations Possibly -|x| ≤ x ≤ |x|, and -|y| ≤ y ≤ |y|? The Attempt at a Solution I tried using a direct proof here, but I keep getting stuck, especially since this is my first time ever coming...
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    Proof of oscillation about the equilibrium

    Ah, I've just realised that the photo quality is significantly decreased by uploading it here. Apologies for that
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    Proof of oscillation about the equilibrium

    I'll try to attach a better photo, but the second p is included in the e+/- 393.75j
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    Proof of oscillation about the equilibrium

    ω is 20 rads-1, from the equation (I have shown it only with values substituted): p = -γ/2 +/- √[ω2 - (γ/2)2] where ω2 = 400 and γ = 5\ And I set x(0) = D, not 0, as x is a function of t, is that incorrect? Thanks
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    Proof of oscillation about the equilibrium

    Homework Statement The problem is question 2(a) in the attached pdf. I seem to find myself at a dead end and am not sure where to go from here - I will attach my working in a separate file, but basically I need to show that the oscillator passes/crosses over the x = 0 boundary at a positive...
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    Solving the General Solution for a Heavily Damped Oscillator

    Homework Statement The question I am working on is number 3 in the attached file. There are two initial conditions given: at time = 0, x(t) = D and x'(t) = v 'in the direction towards the equilibrium position'. Does that last statement mean that when I substitute the second IC in, I should...
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    Derivation of resonant frequency for SHM systems

    Unfortunately I'm not sure what to do once I have the general equations of motion, I'm not looking for someone else to answer my question, just some guidance as to where to go from here :/
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    Derivation of resonant frequency for SHM systems

    file://file/UsersB$/bem60/Home/My%20Documents/2nd%20Year/Phys205/PHYS205%20Assignment%206.pdf ^I have attempted to attach the file, but I doubt it will work unfortunately For the spring question: Equation of motion: ma = -Kx so a +(K/m)x = 0 Energy: Ek = 1/2mv2 And Ep = 1/2Kx2 Total...
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    Derivation of resonant frequency for SHM systems

    Homework Statement My question here isn't a specific question that has been given for homework, but a more general one. For an assignment I have to 'derive an expression for the resonant frequency, ω0' for two different systems, the first for 'a mass M connected to rigid walls via two springs'...
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    Elastic Collision in Two Reference Frames

    Homework Statement 1. Two skateboarders start from rest on opposite sides of a ramp like the one in the image, roll down and collide elastically on the level part of the ramp. The masses of the skateboarders are m1 = 48 kg and m2 = 55 kg and they both start from the height h = 4.70m. Ignoring...
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