Why is that the mass of a pendulum has no effect on its swing period?

Answer 1

I take it you mean the mass at the end of the pendulum?

The pendulum swings back and forth because gravity attracts the mass at the end of the pendulum. It speeds up on its way down and has built up a velocity by time it reaches the bottom. Gravity then slows the object by the exact same rate it sped it up when it was on its downswing. The result is the mass swings back up to the exact same height it started out at (assuming your pendulum has no friction and that there is no air resistance, of course).

As to why the amount of mass doesn't matter: forget about up or down, you just have two objects existing in space. The Earth's gravity pulls the object towards the Earth and the strength of this pull depends on the combined mass of the Earth and the object. The object has some natural resistance to being pulled from its location (i.e. - it has inertia). The mass of the object is its natural resistance to being moved. In other words, the mass is contributing equally to the strength of the force pulling it and to its abilty to resist being moved.

Mathematically, gravitational force is: F=GMm/(r^2) where the force of gravity is F, the universal gravitational constant is G, M is the mass of the Earth, r is the distance from the center of the Earth, and m is the mass of the object.

The effect of this force is expressed by: F=ma where F is the force of gravity, a is how fast the object will accelerate, and m is the mass of the object.

Substituting, you have GMm/r^2 = ma. You have a 'm' on both sides of the equation, meaning mass cancels itself out when you're only concerned with the motion resulting from gravity, not the actual force, itself.

Answer 2

Mass is a measure of Inertia.The higher the mass so is the force required to bring it into motion.Taking earth's mass as reference any other mass -be it a feather or a cannon ball will be insignificant in comparison to it and hence exerts the same gravitational pull upon both objects. The purpose of pendulum of a given mass is only to store energy in a relative proportion to the gravitational force producing constant acceleration upon it while swinging to and fro.The swinging length along an arc when started initially is proportional to the length of hanging string holding the pendulum to one side before releasing.This corresponds to the initial amplitude of oscillations. We observe that the amplitude goes on diminishing as a result of friction acting as a decelerating force at the tieup fulcrum but the period T of each oscillation reaching any one end successively remains the same. This time T is only proportinal to the length of string hanging a pendulum in relation to the accelerated lengths the constant gravitational force would have produced in similar units of length corresponding to gravitational constant.Hence a higher mass of pendulum has no affect on swinging period but due to higher stored up energies potentially at the ends and dynamically at the center allows more swingings overcoming friction before coming to rest.

Answer 3

Though the pendulum oscillates from one end to another end, the motion of pendulum can be explained by conservation of energy.

Join the two extreme positions by a horizontal line and draw a horizontal line along the equilibrium position (Bottom most point on the arc).

The bob is moving between these two lines. When it is in the upper line its speed is zero. It has potential energy. It is pulled by gravity down ward.

When it is in equilibrium position (bottom line), it has maximum kinetic energy. Due to this it goes up against gravity.

Thus the cause of motion of pendulum is the force of gravity and to be more exact it is due to the acceleration due to gravity. The acceleration due to gravity does not depend upon the mass of the bob. Whatever be the mass of bob, it is pulled down with the same acceleration due to gravity. Hence the period does not depend upon the mass of the body.

Answer 4

Sridhar C is rite. The mass of any object is a constant, it does not vary with its surroundings. Therefore the mass of a pendulum has no effect on its swing

Answer 5

Because gravity accelerates the pendulum and is constant.

What matters is how long the pendulum is, because that determines how far the pendulum has to swing.

The longer the pendulum the farther it has to swing and the longer it is going to take to complete one cycle.

Answer 6

attitude shouldnt remember in any respect. imagine about it logically. in case you drop a pendulum from a better attitude, and therefor a better top, it really is going to flow a lot speedier yet has an prolonged distance to flow. on the hather hand, in case you drop a pendlum from a decrease attitude, it really is going to flow slower yet there's a lot less distance to conceal. Thats why both the classes are a similar. you should use F=mv^2/r in case you take advantage of power somewhat of the stress equation although, the position skill engery= gravity*mass*h and kinetic power = (a million/2) *mass*v^2, and the actual undeniable truth that the replace in power is continuously 0, u get mgh=(a million/2)mv^2 accordingly the mass cancels out and is irrelevant to the speed of the pendlum.

Answer 7

Since the mass of any object is a constant, it does not vary with the surroundings.There fore the mass of the pendulum is irrevelant.And the formula,T=2pi*rt(l/g).No mass in it,is there.

Answer 8

mass will not affect time period. that's a law. as for the bob being bigger, well, then the length will change, as the radius will be longer, and thus the Time period increases