Does the period formula work for a V-shaped pendulum?

[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