Pendulums, Simple Harmonic Motion

[Maroon5777]

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I am having a hard time understanding the forces acting on a pendulum. In the princeton review book, it says the restoring force is mgsin(theta). However in another equation, I've seen that ForceTension-mg=mv2/r. I guess what I am saying is I can't seem to differentiate between the restoring force and centripetal force. Are they independent of each other? and also why is tension greatest at bottom? I've looked through many other questions but can't seem to get a grasp of this concept. Would make my day if someone can help.😎

 

[Rabolisk]

Centripetal force only applies if there is uniform circular motion. The fact that it's not uniform means that there is some force in addition to the centripetal force, or, put another way, the net force is not centripetal. What you are describing are really two different circumstances.

Why is tension the greatest at bottom? Because gravity always points down. Think about this.

 

[Truestar01]

If I can remember correctly, the general formula for force on a pendulum is considered to be F = mgsintheta because you know pendulum swings and has x and y components and the restoring force is really taking account the distance displaced. so when you break the components the force in the x direction is mgsintheta. In terms of the other equation, you want to find the force in the y direction which is the force from tension. and the pendulum swings in a centripetal motion, thus they just simplied the acceleration part to v2/r because thats how acceleration is calculated. Thus those two equations apply, it really just depends on what force you are trying to evaluate. the restoring force acts in the x direction. the latter is for y direction.

hope this helps.

I am having a hard time understanding the forces acting on a pendulum. In the princeton review book, it says the restoring force is mgsin(theta). However in another equation, I've seen that ForceTension-mg=mv2/r. I guess what I am saying is I can't seem to differentiate between the restoring force and centripetal force. Are they independent of each other? and also why is tension greatest at bottom? I've looked through many other questions but can't seem to get a grasp of this concept. Would make my day if someone can help.😎

 

[Rabolisk]

If I can remember correctly, the general formula for force on a pendulum is considered to be F = mgsintheta because you know pendulum swings and has x and y components and the restoring force is really taking account the distance displaced. so when you break the components the force in the x direction is mgsintheta. In terms of the other equation, you want to find the force in the y direction which is the force from tension. and the pendulum swings in a centripetal motion, thus they just simplied the acceleration part to v2/r because thats how acceleration is calculated. Thus those two equations apply, it really just depends on what force you are trying to evaluate. the restoring force acts in the x direction. the latter is for y direction.

hope this helps.

Good try, but no..

 

[Truestar01]

hmm, thats interesting.

Good try, but no..

 

[Maroon5777]

Thank you guys for the help thus far. I am still trying to understand the concept. So there are 2 components to the force? The first is the centripetal force, and that ensures that the pendulum moves in a circular path and then the mgsin(theta), the restoring force makes it come back to equilibrium?....so if tension force just a response force or is it there even when no gravity is pulling out on the rod, for instance at 90 degrees to vertical?

 

[Rabolisk]

These are two different situations. The fact that a pendulum follows simple harmonic motion means, by definition, that it is not undergoing uniform circular motion. Ignore what Truestar said about x direction and y direction and so on.

 

[flodhi1]

Thank you guys for the help thus far. I am still trying to understand the concept. So there are 2 components to the force? The first is the centripetal force, and that ensures that the pendulum moves in a circular path and then the mgsin(theta), the restoring force makes it come back to equilibrium?....so if tension force just a response force or is it there even when no gravity is pulling out on the rod, for instance at 90 degrees to vertical?

Dude if it's under going simple harmonic motion it doesn't necessarily mean it has centripetal Force unless it is moving in a circular path. Which could occur on the x component of the simple harmonic motion but that's a very complicated idea. MAKE IT simple don't try to complicate things.

 

[Rabolisk]

If it's undergoing simple harmonic motion, then, by definition, it is not undergoing uniform circular motion. Think about it...

 

[flodhi1]

If it's undergoing simple harmonic motion, then, by definition, it is not undergoing uniform circular motion. Think about it...

Dude Moving around a circle at constant speed is also simple harmonic motion. And when you're moving around a circle at constant speed you will have centripetal force now the key to this is NOT that OH ITS CONSTANT speed thus acceleration is 0 and magically NO centripetal force. Acceleration occurs due to change in direction since Acceleration is a VECTOR even if the magnitude of the speed is constant because the direction changes in a simple harmonic motion such as circular motion you WILL HAVE centripetal acceleration. Thus you CAN have simple harmonic motion and centripetal force, I would suggest you grab a Physics text book and re-evaluate your statement.

 

[Rabolisk]

Dude Moving around a circle at constant speed is also simple harmonic motion. And when you're moving around a circle at constant speed you will have centripetal force now the key to this is NOT that OH ITS CONSTANT speed thus acceleration is 0 and magically NO centripetal force. Acceleration occurs due to change in direction since Acceleration is a VECTOR even if the magnitude of the speed is constant because the direction changes in a simple harmonic motion such as circular motion you WILL HAVE centripetal acceleration. Thus you CAN have simple harmonic motion and centripetal force, I would suggest you grab a Physics text book and re-evaluate your statement.

I meant SHE in the case of a pendulum swinging from one side to other, where mgsintheta as the restoring force would apply. I should have been a bit more careful in my statements, though. You are right that a uniform circular motion of any kind is SHE when viewed in one direction.

Also, after thinking more about this, I suppose that in such a pendulum, when it is directly at the bottom (theta = 0), there is uniform circular motion AT THAT INSTANT, and the force is exactly centripetal and points directly in the y direction towards the center. The rationale for this is that the velocity vector does change direction, even while the restoring force is exactly 0, so there must be a centripetal force.