How Does Pivot Point Location Affect the Time Period of a Physical Pendulum?

In summary, the conversation discusses a problem involving a spring-mass oscillation and a horizontal lever with a weight attached. The participants discuss the forces and moments involved, with the mentor suggesting an equation of motion using the moment exerted by the spring and the moment of inertia of the rod. The mentee presents a diagram and equation of motion, which is confirmed to be correct by the mentor.
  • #1
Yossi33
22
3
Homework Statement
Physical pendulum time period
Relevant Equations
T=2pi*(I/mgh)
hello, i have some diffuculties with this problem, there's the point where the spring is attached to the rod and according to the equation of time period of physical pendulum , h represent the distance from the COM and the pivot point. here the pivot point is at the COM. and i know that it can't be (then the T would be infinity). i don't know if i need to calculate the T of the spring and it would be the same but than what part of the mass is attached to it.
thanks for the help.
https://ibb.co/nsGTrQw

[Mentor Note -- Newbie OP reminded to upload images to PF to avoid confusion when externally linked images disappear (and the associated suspicions of student cheating). All associated images have been uploaded by the Mentors]
1647018355455.png
 
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  • #2
It looks more like a spring-mass oscillation problem than a pendulum problem to me. Can you show us your FBD for the horizontal lever during small oscillations?
 
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  • #3
I think you need some specific analysis and an equation of motion for this problem.
 
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  • #4
berkeman said:
It looks more like a spring-mass oscillation problem than a pendulum problem to me. Can you show us your FBD for the horizontal lever during small oscillations?
https://ibb.co/LPhzYhf
you mean like this? it's an overhead view so the weight and normal cancel each other so there is only the kx of the spring.

1647018429135.png
 
  • #5
Yossi33 said:
https://ibb.co/LPhzYhf
you mean like this? it's an overhead view so the weight and normal cancel each other so there is only the kx of the spring.
That's a good start.
 
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  • #6
PeroK said:
That's a good start.
but how can i express the partial mass of the rod that is attached to the rod?
 
  • #7
What have you learned about moments?
 
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  • #8
pbuk said:
What have you learned about moments?
the force by the spring exert a moment on the rod equal to F*(half length of rod) ( the perpendicular distance for the line of action of the force and the rotation axis)
if i denote the rod L and F is kx then
the moment about the rotation axis , exerted by the spring is kx*0.5*L
 
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  • #9
And what resists the moment exerted by the spring?
 
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  • #10
do you mean the screw at the center of the rod?
 
  • #11
Yossi33 said:
do you mean the screw at the center of the rod?
I think he meant the moment of inertia!
 
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  • #12
PeroK said:
I think he meant the moment of inertia!
Yes. So can you write an equation of motion using the moment exerted by the spring and the moment of intertia of the rod?
 
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  • #13
pbuk said:
Yes. So can you write an equation of motion using the moment exerted by the spring and the moment of intertia of the rod?
https://ibb.co/kgYgSL9 is it correct?

1647049718000.png
 
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  • #15
thank you all for the help
 
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Related to How Does Pivot Point Location Affect the Time Period of a Physical Pendulum?

What is a physical pendulum?

A physical pendulum is a mechanical system that consists of a rigid body suspended from a fixed point and allowed to swing back and forth under the influence of gravity.

What is the time period of a physical pendulum?

The time period of a physical pendulum is the time it takes for one complete swing or oscillation of the pendulum.

How is the time period of a physical pendulum calculated?

The time period of a physical pendulum can be calculated using the formula T = 2π√(I/mgd), where T is the time period, I is the moment of inertia of the pendulum, m is the mass of the pendulum, g is the acceleration due to gravity, and d is the distance between the pivot point and the center of mass of the pendulum.

What factors affect the time period of a physical pendulum?

The time period of a physical pendulum is affected by the length of the pendulum, the mass of the pendulum, and the acceleration due to gravity. It is also affected by the angle of displacement and the air resistance.

How can the time period of a physical pendulum be increased?

The time period of a physical pendulum can be increased by increasing the length of the pendulum, increasing the mass of the pendulum, or decreasing the acceleration due to gravity. Additionally, reducing the angle of displacement and minimizing air resistance can also increase the time period.

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