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

In summary, the conversation discusses a problem involving a hinged rod with an object attached to the end and a slight disturbance causing it to fly down. The question being addressed is how long it takes for the object to reach the minimum point. The conversation also mentions the use of a diagram and setting up a differential equation to solve for the time. However, the use of energy methods is not helpful and the assumption of small amplitude vibrations does not hold in this problem. Suggestions are made to use Newton's 2nd law to write down the equation of motion, but it is not an easy equation to solve.
  • #1
thereddevils
438
0

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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  • #2
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.
 
  • #3
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.
 
  • #4
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.
 
  • #5
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?
 
  • #6
can i get more help on this?
 
  • #7
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.
 

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

What is simple harmonic motion?

Simple harmonic motion is a type of periodic motion where the restoring force is directly proportional to the displacement from equilibrium. This means that the object will oscillate back and forth around a central point, with the same period of oscillation and amplitude each time.

What are some examples of simple harmonic motion?

Some examples of simple harmonic motion include the motion of a pendulum, a mass on a spring, and the motion of a mass attached to a vertical hanging spring. Any object that follows Hooke's Law, which states that the restoring force is directly proportional to the displacement, will exhibit simple harmonic motion.

What is the equation for simple harmonic motion?

The equation for simple harmonic motion is x = A*cos(ωt+φ), where x is the displacement from equilibrium, A is the amplitude, ω is the angular frequency, and φ is the phase constant. This equation describes the sinusoidal motion of the object.

What is the relationship between period and frequency in simple harmonic motion?

The period of a simple harmonic motion is the time it takes for one complete oscillation, while the frequency is the number of oscillations per unit time. The relationship between the two is T = 1/f, where T is the period and f is the frequency. This means that as the frequency increases, the period decreases, and vice versa.

How does amplitude affect simple harmonic motion?

The amplitude of simple harmonic motion is the maximum displacement from equilibrium. A larger amplitude will result in a greater maximum velocity and acceleration, but the period and frequency will remain the same. In other words, changing the amplitude does not affect the time it takes for one complete oscillation.

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