How do different string lengths compare in different pendulums?

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electreto05 | College Teacher | (Level 1) Assistant Educator

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The pendulum is a physical system which can oscillate under the action of gravity or other physical action such as an elastic force. In its simplest form, it consists of a body of mass m, suspended from a fixed point or horizontal axis, by a rope, rod, or other device. The most common use of the pendulum is to measure time.

The most important parameter of a pendulum is the period T, which is the time at which a complete oscillation is performed. The Italian astronomer Galileo Galilei observed that the oscillation period of a pendulum is independent of amplitude (separation from the equilibrium position), at least for small oscillations; but it was dependent on the length of the rope. The relationship between the period of oscillation of the pendulum and its length is written as follows:

T = 2π sqrt(l/g)

Where:

l, is the length of the rope.

g, is the acceleration of gravity in the place where the pendulum is.

So that, the period of oscillation is proportional to the square root of the length. To apply this expression to a pendulum, it must meet the following conditions:

. The rope must be inextensible and massless.

. The body suspended, should have negligible mass.

. The oscillations must take place in a single vertical plane.

. The angle of separation of the equilibrium position should be very small.

From the experimental point of view, the pendulum is a very useful device to measure gravity. In practice it is useful to set time intervals, very accurately.

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