Question

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

Answer 1

Answer:

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.

Answer 2

Definition:

Ideal simple pendulum is defined as a heavy point with mass suspended by a weightless string and oscillate in SHM motion under gravity.

Expression:

let, m be the mass of the pendulum.

L be the length of the string.

F be the force on the pendulum.

T be the time period of the pendulum.

p be the tension on the string.

g be the acceleration due to gravity.

now, p = mg cos∅

for small angle cos∅ = 1

so, F = mg sin∅

for object in SHM

g∅ = ω^2 x  ( x is displacement)   ------1

and x = L∅      -------2

from 1 and 2

g = ω^2L

g = (2π/T)^2L  since ω = 2π/T

T = 2π√L/g

Time period of a pendulum is the time taken by a pendulum to complete one SHM motion.