V-Shaped Pendulum Help - Formula & Analysis

[PhysicsLearne]

Hey there,

Basically we had an experiment where we had to change the distance 'd' on a v shaped pendulum (0.5d for each side of the V)..where the value 's' which is the hypotenuse distance of the V stayed constant but the vertical distance changed.

does the following formula hold:- we know T = 2pi√L/g

now for this experiment using pythagorus' theorem we can find that L = s^2 - 0.25d^2

which gives T = 2pi√√s^2 - 0.25d^2 / g

is this correct and does the equation hold.

also what other things can i talk about to analyse V-shaped pendulums in particular, I have to write a long essay on it. and was wondering what else i could say the experiment.

Thanks a lot

 

[wywong]

If you look along the line joining the 2 end points of the "V", you can see that the locus of the weight is no different from that of a typical pendulum with length L. At every corresponding point the potential energy of the weight is the same in either type. By conservation of energy, the velocity of the weight must also be the same. So the two types behave the same and your work looks good to me.

The V-shaped pendulum confines the periodic motion in only one plane which may be convenient for most applications. A typical pendulum's plane of motion depends on initial conditions and changes over time due to Foucault pendulum precession. If started improperly, the latter can be set to swing in a vertical plane while circling in a horizontal plane at the same time.

Wai Wong

 

[astrokreng]

Hello there,

First of all, it is important to note that the formula for the period of a pendulum, T = 2π√L/g, is only valid for a simple pendulum where the mass is concentrated at a single point and the length of the pendulum is much longer than the amplitude of its swing. In a V-shaped pendulum, the mass is distributed along the arms of the V and the length of the pendulum is not constant, so this formula may not hold true in this case. It is important to consider the specific characteristics of the V-shaped pendulum when analyzing its behavior.

In terms of your proposed formula, T = 2π√√s^2 - 0.25d^2 / g, it is not entirely correct. The square root should only be applied to the value inside the parentheses, so it should be T = 2π√(s^2 - 0.25d^2) / g. However, this formula still assumes that the mass is concentrated at a single point, so it may not be accurate for a V-shaped pendulum.

To further analyze V-shaped pendulums, you could consider the effect of the angle of the V on the period of the pendulum. Does changing the angle affect the period in any way? You could also investigate the effect of changing the mass distribution along the arms of the V. How does this affect the period and other characteristics of the pendulum's motion?

Additionally, you could look into the energy transfers that occur in a V-shaped pendulum and how they differ from a simple pendulum. How does the kinetic energy and potential energy change as the pendulum swings? Are there any points where the energy is maximum or minimum? This can also tie into the analysis of the pendulum's motion and how it is affected by different factors.

Overall, there are many aspects of V-shaped pendulums that can be explored and analyzed in your essay. I would suggest researching various sources and studies on V-shaped pendulums to gather more information and ideas for your essay. Good luck!