Tue February 21, 2012 By: Vishnu Ms

while doing simple pendulum experiment,a boy arguied that a period of ocsillation not only depent on length and gravity but also depent on mass of a bob

Expert Reply
Wed February 22, 2012
The period of oscillation of a pendulum is dependent only on two factors - length of the pendulum and the gravitational force of the earth. The period increases with the increase in length, and decreases with increase in gravitational force. The mass of the bob has no effect on speed of the pendulum. Similarly the amplitude of the pendulum - that is the distance between two extreme points of the arc -  has no impact on speed of the pendulum.

The gravitational force of the earth at any place remains constant. Therefore at any given place the period of the pendulum is dependent only on length of pendulum. The gravitational force reduces slightly as we move to higher altitudes, and therefore the pendulum of same length will have slightly longer period at higher altitudes.

A  248.7 mm long simple pendulum will have a period of one second at sea level. This period will double if the length is made four times, and triple if length is made nine times.

We say normally say acceleration and velocity at any point of time , or when the pendulum is at a point on its path of oscillation:

Acceleration = -conxtant times the distance from the fixed point. Alternatively,the rate of change of velocity = -constant times distant from the fixed point.

From the above we can arrive at the velocity of the oscillating pendulum at an instant on ts path:

Velocity = square root of (square of half the amplitude - square od its distance drom the fixed point).

If v is the velocity of the pendulum at any time t and the distance is x from the fixed  ( or mid point of the amplitude). then:

v = square root(a^2-x^2), where a is the half amplitude.

By this, we see that the velocity of the pendulum at any point of time is independent of the mass of the pendulum. But the velocity is dependent on the and a factors.

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