Question

SHM, Small-angle approximation problem?? Please helpp...

Answer 1

I can do the first part, the one with moment of inertia, but I can't understand the second part at all....

Answer 2

Here is the answer key to the question

Answer 3

\[\sin \theta = \theta-\frac{ 1 }{6 }\theta ^{3}+...higher ~terms~ of~\theta \]
\(\theta\) is radian...
if \(\theta\) is very small then higher terms of \(\theta\) including \(\theta^3\) are negligible..
so sin\(\theta\) ~ \(\theta\)

Answer 4

I don't understand the line before it, the one with the differential equation involving second derivative of angular displacement

Answer 5

the right hand side of that equation is the net torque about the point C perpendicular to the plane of the ring

Answer 6

(moment of inertia about the axis)*(angular acceleration about the same axis)=(net torque about that axis)
the torque is due to the weight of the sphere,rod and ring..

Answer 7

Thanks a lot!