Recent content by jimz

"The net work done by all the forces acting on a body equals the change in its kinetic energy." Not seeing it...

Homework Statement A particle with total energy E and mass m is subject to a force F(x)=\xi x^4. Find the velocity v of the particle as a function of the position x, and sketch a phase diagram for the motion. Homework Equations T=\frac{1}{2}m\dot{x}^2 U=constant F=m\ddot{x} The Attempt at a...

Your observation that you do not need time to solve the problem is correct. The observation that all those equations involve time is not- look carefully.

Still can't see what I did wrong... how does the 4a not become a?

Thanks! I forgot that dθ/dt is ω and it's the chain rule twice. So close, but why am I off... -\frac{1}{4}\omega^2u+\frac{g}{4a}u=0 \frac{1}{4}\omega^2=\frac{g}{4a} \omega=\sqrt{\frac{g}{a} T=\frac{2\pi}{\omega}=2\pi\sqrt{\frac{a}{g}

I'm sure that the equation of motion is correct. It's long and uses some tricky trig identities, but more importantly it matches the answer as given. In any event, it's the period of oscillation part I do not understand.

Homework Statement Find the period of oscillation of a bead on a cycloid string. If it matters, the original equations of the cycloid were x=a(\theta-sin\theta) and y=a(1+cos\theta) Homework Equations This is a small part of a larger problem... I found the equation of motion of a bead on a...

I'm having a bit of a hiccup understanding the differentiation that I am doing... I'd like to be clear on the concept rather than just knowing 'apply chain rule'. So I have a particle with equation: y=a(1+cos\theta) now the derivative with respect to time (the velocity in y) is...

yes, it's a problem from our book. Does that matter? I now think I set it up correctly and it's now just a math problem but I still can't get anywhere closer to the solution for theta.

Homework Statement A string through an ideal pulley connects two blocks, one (mass=2m) is on an inclined plane with angle theta to horizontal and coefficient of kinetic friction mu. The other block (mass=m) hangs off the pulley on the high side of the inclined plane. (looks like this, except...

I'm trying to follow a very simple example example in a text (Marion/Thornton example 2.1) and I think my rusty calculus is tripping me up and I'm just being stupid. I understand how to derive the acceleration down the plane: \ddot{x}=g\sin\Theta but next they say 'we can find the...