Why do we use Sinθ θ while finding the time period of a simple pendulum?

If it is a pendulum, amplitude must be small because the “time period does not depend on amplitude” rule applies to pendulums only if it is exhibiting simple harmonic motion. So, when amplitude is kept small (allowing use of the sinθ=θ approximation), time period is independent of amplitude.

Why does the angle the pendulum is pulled from the equilibrium position not affect the period of the pendulum?

Why does the angle the pendulum starts at not affect the period? (Answer: Because pendulums that start at a bigger angle have longer to speed up, so they travel faster than pendulums that start at a small angle.)

Why does angle affect the period of a pendulum?

The longer the length of string, the farther the pendulum falls; and therefore, the longer the period, or back and forth swing of the pendulum. The greater the amplitude, or angle, the farther the pendulum falls; and therefore, the longer the period.)

What is simple pendulum obtain an expression for time period of simple pendulum?

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.

What is time period of simple pendulum?

The time period of a simple pendulum: It is defined as the time taken by the pendulum to finish one full oscillation and is denoted by “T”. The amplitude of simple pendulum: It is defined as the distance travelled by the pendulum from the equilibrium position to one side.

What does the time period of a simple pendulum depends on?

The only things that affect the period of a simple pendulum are its length and the acceleration due to gravity. The period is completely independent of other factors, such as mass.

What does the time period of a simple pendulum depend on?

the length of
Note: The time period of the simple pendulum depends upon the length of the pendulum and also to some extent it depends upon the degree of the amplitude. That is the width of the pendulum’s swing. In general, the time period of a pendulum means one complete cycle that is one complete left swing and right swing.

What is the expression for the time period of a simple pendulum?

What is the motion of a simple pendulum?

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 gravitational force.

How do you find the period of a simple pendulum?

For small oscillations the period of a simple pendulum therefore is given by T = 2π/ω = 2π√(L/g). It is independent of the mass m of the bob. It depends only on the strength of the gravitational acceleration g and the length of the string L. By measuring the length and the period of a simple pendulum we can determine g.

Is the energy of a pendulum constant over time?

However, the total energy is constant as the function of time. In a simple pendulum, the mechanical energy of the simple pendulum is conserved. If the temperature of a system changes then the time period of the simple pendulum changes due to a change in length of the pendulum.

What is the acceleration due to gravity when a pendulum is moved?

A simple pendulum with a period of 2.00000 s in one location where g = 9.80 m/s 2 is moved to a new location where the period is now 1.99796 s. What is the acceleration due to gravity at its new location? Solution: For a simple pendulum the period T = 2π)/ω is proportional to 1/g 1/2.

How do you find the angular displacement of a simple pendulum?

By measuring the length and the period of a simple pendulum we can determine g. s = Lθ. The angular displacement of a pendulum is represented by the equation θ = 0.32*cos (ωt) where θ is in radians and ω = 4.43 rad/s. Determine the period and length of the pendulum.