time period of a simple pendulum depends on the acceleration due to gravity mass of the pendulum and length of the pendulum find the powers
Answers
Explanation:
How is the expression of a time period of a simple pendulum, when it depends on the mass, length, and acceleration due to gravity?
The mass of the body m is not affecting the period of a simple pendulum. Below is the equation of the period of a simple pendulum.
T is the period of the simple pendulum. L is the length of the pendulum and g is the acceleration due to gravity. 2 and pi are numbers. The period of a simple pendulum is directly proportional to the square root of its length and is inversely proportional the the square root of g.
The period of a simple pendulum depends only on length and the acceleration of gravity, not on mass.
The question is ambiguous because of the unconventional grammar.
If the question is “what is the expression for the period of a simple pendulum” the answer, for infinitesimally small displacements, is T= 2 pi sqrt(L/g)
If the question is “how do you derive the expression for the period of a simple pendulum” the answer is more complicated. To begin with, F=Ma, but also F=MgL sin theta. When you combine the two expressions for F, F drops out, and so does M. The acceleration a is the derivative of velocity, which is the derivative of position, which is approximately (L theta). For small displacements, sin theta is approximated by theta, so you get a second order linear differential equation that is a form of the equation for simple harmonic motion.