Calculating Time for Simple Harmonic Motion: Rod with Freely Rotating Object

[thereddevils]

Homework Statement

Given a rod with length it is hinged thus it can freely rotate. An object is attached to the end of the rod and it is brought all the way vertically up. Then a slight disturbance and it flies down (from equilibrium). How long does it take for it to come down to the minimum point?

Homework Equations

The Attempt at a Solution

I need a simple diagram to visualize the problem better.

 

[The legend]

Try drawing it out yourself and post it here... as per PF rules you got to do something on your own before you get any help.

 

[thereddevils]

Try drawing it out yourself and post it here... as per PF rules you got to do something on your own before you get any help.

Well, i will try to describe my diagram. It's similar to the diagram of the oscillation of a simple pendulum but now the string is replaced with the rod held at its maximum point at t=0 before release. Then, i tried to set up a DE.

Total energy = kinetic energy + potential energy

What confuses me here is the kinetic energy, i am not sure whether it's the kinetic energy during simple harmonic motion (1/2 mw^2 (x0^2 -x^2)) or the rotational kinetic energy (1/2 Iw^2)?

I will post further attempts after i clear this part. Thanks.

 

[vela]

Since you're looking for a time, energy methods generally aren't very helpful. Also, for a pendulum, simple harmonic motion follows from the assumption of small amplitude vibrations — in other words, when θ is small. In this problem, that assumption doesn't hold.

 

[thereddevils]

Since you're looking for a time, energy methods generally aren't very helpful. Also, for a pendulum, simple harmonic motion follows from the assumption of small amplitude vibrations — in other words, when θ is small. In this problem, that assumption doesn't hold.

Thanks, can you suggest the correct way of doing this?

 

[thereddevils]

can i get more help on this?

 

[vela]

You can apply Newton's 2nd law to write down the equation of motion for the system, but the resulting equation isn't easy to solve.