Derivation of simple pendulum formula

In summary, the simple pendulum formula is a mathematical equation that describes the motion of a pendulum. It is derived by using the principles of circular motion and simple harmonic motion. The formula is affected by the length of the pendulum, the acceleration due to gravity, and the amplitude of the swing. However, it can only be used for idealized pendulums and has limitations such as neglecting friction and air resistance, and not accounting for the mass or shape of the pendulum. These limitations may result in slight discrepancies between the predicted and actual period of a pendulum.
  • #1
physicsgal10
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You pull a simple Pendulum of length 0.240 m to the side through an angle of 3.5 degrees and release it.
(a) How much time does it take the pendulum bob to reach its highest speed?
(b) How much time does it take if the pendulum is released at an angle 1.75 degrees instead of 3.5 degrees?
 
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  • #2
Draw a free body diagram so you can write the differential equation for the motion of the pendulum bob. Assume small angle of swing so you can get a differential equation that you can easily solve.
 

1. What is the simple pendulum formula?

The simple pendulum formula is a mathematical equation that describes the motion of a pendulum. It is given by T = 2π√(l/g), where T is the period of the pendulum, l is the length of the pendulum, and g is the acceleration due to gravity.

2. How is the simple pendulum formula derived?

The simple pendulum formula is derived by using the principles of circular motion and simple harmonic motion. By analyzing the forces acting on a pendulum, such as gravity and tension, the equation for the period of a pendulum can be derived.

3. What factors affect the period of a simple pendulum?

The period of a simple pendulum is affected by the length of the pendulum, the acceleration due to gravity, and the amplitude of the swing. A longer pendulum will have a longer period, while a stronger gravitational force or a larger amplitude will result in a shorter period.

4. Can the simple pendulum formula be used for any type of pendulum?

No, the simple pendulum formula is only applicable to idealized pendulums, which have a small amplitude of swing and a point mass at the end of the pendulum. Real-life pendulums, such as a physical pendulum or a compound pendulum, require more complex equations to describe their motion.

5. What are the limitations of the simple pendulum formula?

The simple pendulum formula assumes that there is no friction or air resistance acting on the pendulum, which is not always the case in real-life situations. Additionally, the formula only applies to small angles of swing and does not take into account the mass or shape of the pendulum. These limitations may result in slight discrepancies between the predicted and actual period of a pendulum.

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