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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...

Yes I had, thank you. I'll have another try!

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...

Oh, that was dumb. Thank you!

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...

Thank you all for your replies :)

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...

Ah, I've just realized that the photo quality is significantly decreased by uploading it here. Apologies for that

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

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

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...

Thank you!

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...

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 :/

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...

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'...

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...