Pendulum Frequency and Velocity

[September24]

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1.Should an increase in frequency mean an increase in pendulum velocity.

For example, decreasing the length of the pendulum would indicate that the period will go down. If the period is shorter, isn't the pendulum moving faster? Therefore, will a shorter length indicate a faster velocity?

2. Furthermore, what factors influence the restoration force on a pendulum. I know its displacement angle but I was wondering if anything has an input.

3. Does restoration force have an impact on maximum velocity?

 

[DrknoSDN]

1. The rotation around the axis is faster but that will alter acceleration (net force at time T), not maximum velocity.

- Imagine a pendulum arm perpendicular to the ground with a length so long that it is not subjected to any observable rotation (it falls almost straight down), any arm that is shorter where the rotation is observable would have increased acceleration due to any centripetal force from changing direction.
The max velocity would be largely determined by how much time it took for the pendulum to go from zero kinetic energy to minimum potential energy.
Longer arms allows more time for gravity to exert a force on the pendulum so higher max velocity.

2. Tension (http://www.physicsclassroom.com/class/waves/Lesson-0/Pendulum-Motion)

3. Yes, like i described in 1, if a very long pendulum arm caused the pendulum to fall essentially directly towards the gravitational source (theoretically) there would be a near-infinite max velocity because the tension is the only force that counters the acceleration from gravity, and tension would be near-zero.


*Sorry if example is not exactly "real world". But if you look at trends towards infinities you can make comparisons to the finite more easily.

 

[September24]

Hey Dr.KnoSDN! Thanks for your help. Unfortunately Im still a bit confused. You bring up an interesting point. The force in pendulum motion is mainly centripetal force? Therefore, restoration force for a pendulum=mgsin=mv^2/r

If the length is shorter, then there will be a larger force which means a larger maximum velocity? Or maybe I just proved the T=2pisqrt(l/g). Decreases L here also decreases time and increases velocity.

I'm basically making things concrete just in case mcat decides to ask one of those "If I change X, what changes...?" type of questions. If length is shortened, I know that period will be changed but I'm not so sure about velocity or force.

 

[September24]

Also. side question. I know that as we approach equilibrium, velocity increases as potential energy is converted to kinetic.

However, restoration force decreases as we approach equilibrium. If it makes sense that the velocity increases since even though accelerationi may decrease as we approach equilibrium, the pendulum still accelerations by a smaller amount so velocity will still be increasing. However,

F=mv^2/r
By this equation, force decreasing should decrease velocity...Or maybe it is change in velocity? That would make more sense.

Sorry, I've been focusing on electrostatics lately so my mind if fried (no pun intended) by that. I feel like I forgot a basic concept getting lost in statics.

 

[ipmed]

Pendulum is periodic motion and it has max velocity and eq or point closest to source of force, but the force is smallest here by f=kx. Height is proportional to the velocity by conservation of energy