Question

• Define simple pendulum. Deduce an expression for period of simple pendulum. Hence state the factors on which its period depends.​

Answer 1

Answer:

The simple pendulum is another mechanical system that moves in an oscillatory motion. It consists of a point mass 'm' suspended by means of light inextensible string of length L from a fixed support as shown in Fig. 2.8. The motion occurs in a vertical plane and is driven by a gravitationa

A mass m suspended by a wire of length L is a simple pendulum and undergoes simple harmonic motion for amplitudes less than about 15º. The period of a simple pendulum is T=2π√Lg T = 2 π L g , where L is the length of the string and g is the acceleration due to gravity.

time period of simple pendulum depends upon the length of the pendulum, acceleration due to gravity and the temperature (as length depends on temperature). It is directly proportional to the square root of length and inversely proportional to the square root of acceleration due to gravity.

Answer 2

Simple Pendulum - A simple pendulum is heavy point mass(bob) suspended from a rigid support by a massless and an inextensible string. This is an ideal case because we cannot have a heavy mass having the size of a point and a string which is massless.

Time Period of simple pendulum :-

     T = 2π√l/g or T² = 4π²l/g

The factors on which time period is dependent are:-  

a) The time period of oscillation is directly proportional to the square root of its effective length.

T ∝ √l or T² ∝ l   i.e (time is directly proportional to the square root of length of the pendulum.)

b) The time period of oscillation is inversely proportional to the square root of acceleration due to gravity.

T ∝ 1/√g