An undamped pendulum of mass m = 10kg, and length L = 5m, is released at time t = 0 with an initial displacement θ(0) = 0.05 radians and an initial angular frequency ω(0) = 0.1 radians/s.
I need to calculate the amplitude of the oscillations in radians, and the total energy of the oscillations...
Thanks, I did the second step of the parts with the wrong inspection method (used the log method instead of the raise the power and check co-efficient method). I'm now at the right answer, thanks for your help everyone, and thanks for that website too. Also about the arcsinh thing, we've been...
Thanks for that, I got the following final answer:
\frac{1}{2}. (x^2 .arsinh(x^2) - ln(1+x^4)^{0.5}) +C
Oh and why let u=arcsin(x) for the sub? I assume you meant arsinh and just misread?
Hi guys, I don't even know where to begin with this question.
Find the following indefinite integral:
\int x.arsinh (x^2) dx
Thanks very much for any help, its much appreciated.
Thank you very much for that, my final answer of
\frac{dy}{dx} =-\frac{x}{\sqrt{a^2-x^2}}
Agrees with the answer obtained if you just differentiate 'normally'. Thanks again!
Hey guys, I've got the following 2 mark question on a problem sheet, but I can't seem able to do it. I'd appreciate any help, thanks.
Differentiate, from first principles, the following:
y=\sqrt(a^2-x^2)
I know I have to take the limit as δx tends to 0 of [(f(x+δx)- f(x)]/δx but can't seem to...