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...
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...
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...
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...
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...
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 :/