Just come across a question and I'm at a point where i see no further.
A uniform rod AB, of mass m and length 2a, is free to rotate in a vertical plane, about the end A. A light elastic string of modulus kmg and natural length a, has one and attached to B and the other end to a fixed point O...
A particle P of mass 0.2kg is attatched by an elastic spring of modulus 15N and natural length 1m to a point A of the smooth horizontal surface on which P rests. P recieves an impulse of magnitude 0.5Ns in the direction AP. Show that while the string is taught, the motion of P is simple harmonic...
This is probably a really easy question. But alas the answer has eluded me thus far. Anyway, here is the question:-
Points O, A and B lie in that order on a straight line. A particle P is moving on the line with S.H.M period of 4s, amplitude 0.5m and centre O. OA is 0.1m and OB is 0.3m. When...
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A particle P of mass m is attached to one end of a light elastic string of natural length L whose other end is attached to a point A on a ceiling. When P hangs in equilibrium AP has length \frac{5l}{3}. Show that if P is projected vertically downwards from A with speed \sqrt(\frac{3gl}{2}), P...
A particle P of mass m is attached to one end of a light elastic string of natural length L whose other end is attached to a point A on a ceiling. When P hangs in equilibrium AP has length \frac{5l}{3}. Show that if P is projected vertically downwards from A with speed \sqrt(\frac{3gl}{2}), P...
\frac{dv}{dt}= -x^{-3}
when t=0, the particle is at rest with x=1
Therefore by integrating i get
v = \sqrt(x^-2 - 1)
\frac{dx}{dt}= \sqrt(\frac{1 - x^2}{x^2})
dx\frac{x}{(/sqrt(1 - x^2))} = dt
-\sqrt(1 - x^2) = t + C
C=-1
Therefore:-
t = 1 - \sqrt(1 - x^2)
However i cant...
Hey.
I've been doing more mechanics recently - further kinematics in M3. I've come across another question i'm confused by.
A particle moves on the positive x-axis. When its displacement from O is x meters, is acceleration is of magnitude x^-3 m/s^2 and directed towards O. Given that...
I'm studying M3 as one of the three modules for my further maths alevel, and have just started the first chapter. I'm fine with acceleration as a funtion of time, and integrating to find velocity and displacement, and most of acceleration as a function of displacement, but have come stuck on one...
Just came across a question today with 2^x and realised i didnt know how to differentiate it. The entire function i had to differentiate was
[math]y = 2^x + x -4[math]
I tried taking logs but couldnt get anywhere near the true answer.
What is the correct method for this?
Thank's alot!
I just came across this one, was going really well until i came across this one.
(d^2y/dx^2) + (dy/dx) = e^(-x)
m^2 + m = 0
m = -1 and m = 0
Now i get the particular integral
Try y = ke^(-x)
(dy/dx) = -ke^(-k)
(d^2y/dx^2) = ke^(-x)
ke^(-x) - ke^(-x) = e^(-x)
I get stuck here...
Just need a hand with this one.
(dy/dx)x + 2y = x^3.ln(x)
(dy/dx) = (x^3.ln(x) - 2y)/x
Integrating factor = x^2
(dy/dx)x^2 + 2xy = (x^3.ln(x))x^2
yx^2 = INT[(x^3.ln(x))x^2]
I'm having trouble integrating the last part to complete it.
Thanks alot and in advance for any help.
Just working through my FP1 book and have got stuck on a question.
Use the identity (r+1)^3 - r^3 \equiv3r^2 + 3r + 1
to find \sum\limits_{r = 1}^n r(r+1)
I've tried using the method of differences to get n^3 + 3n^2 + 3n, but cant see how to get it back into its original form, not sure how...