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

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Homework Help Overview

The problem involves a rod that is hinged and can freely rotate, with an object attached to its end. The scenario describes the object being raised vertically and then released, prompting a discussion on calculating the time it takes to reach the minimum point after a slight disturbance.

Discussion Character

  • Exploratory, Conceptual clarification, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the need for a diagram to visualize the problem and explore the setup of a differential equation. There is confusion regarding the appropriate form of kinetic energy to use in the context of simple harmonic motion versus rotational motion.

Discussion Status

Some participants have provided guidance on the limitations of energy methods for this problem and noted the importance of the small angle approximation in simple harmonic motion. Others have suggested using Newton's second law to derive the equations of motion, although they acknowledge the complexity of the resulting equations.

Contextual Notes

Participants are navigating the constraints of the problem, particularly the assumption of small amplitude vibrations which may not apply in this case. There is an emphasis on the requirement for initial personal effort before receiving assistance, as per forum rules.

thereddevils
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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.
 
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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.
 
The legend said:
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.
 
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.
 
vela said:
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?
 
can i get more help on this?
 
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.
 

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