Period of a two-mass pendulum?

Question

Given a two-mass pendulum, that is, two masses attached to a rod (of negligible mass) with the pivot point at the middle of the rod, what is the period of the pendulum when released from rest (with the rod horizontal) if one mass is 200 g, the other is 100 g, and the length of the rod from the midpoint to each mass is 20 cm (the rod is 40 cm long in all)?

Answer 1

The period of the pendulum is related through its physical properties by the equation

T = 2 pi sqrt ( I / mgd )

where T is the period, I the moment of inertia, m the total mass, g the local acceleration of gravity, and d the distance between the pivot point and the center of mass.

The moment of inertia of a point mass m at a distance r from the center of rotation is m r^2. Fortunately, the rod is of neglible mass. So you need to do is find the center of mass of the system. Relative to the 200 g mass, it is at

x = 100 * 20 cm / 300.

The difference between x and the center of the rod is d.
Use the distances between x and the masses to compute the total moment of inertia (m r^2 for each). Then plug everything into the first equation to get the period.

Answer 2

Mass is a level of Inertia.the better the mass so is the tension required to deliver it into action.Taking earth's mass as reference the different mass -be it a feather or a cannon ball would be insignificant in assessment to it and for this reason exerts a similar gravitational pull upon the two products. the point of pendulum of a given mass is merely to save capability in a relative proportion to the gravitational tension producing consistent acceleration upon it on a similar time as swinging from facet to facet.The swinging length alongside an arc while started initially is proportional to the dimensions of putting string retaining the pendulum to a minimum of one facet previously liberating.This corresponds to the preliminary amplitude of oscillations. We be conscious that the amplitude is going on diminishing as a effect of friction appearing as a decelerating tension on the tieup fulcrum however the era T of each and every oscillation achieving anybody end successively maintains to be a similar. This time T is merely proportinal to the dimensions of string putting a pendulum in terms of the sped up lengths the consistent gravitational tension might have produced in comparable instruments of length equivalent to gravitational consistent.for this reason a more suitable mass of pendulum has no impact on swinging era yet with the aid of bigger saved up energies doubtlessly on the ends and dynamically on the middle facilitates extra swingings overcoming friction previously coming to kick back.