Simple Pendulum Problem: Solving for Amplitude without Small Angle Approximation

In summary, a simple pendulum is a weight suspended from a fixed point by a string or rod, and is used to study pendulum behavior and conduct physics experiments. Its motion is governed by the law of conservation of energy and is affected by factors such as string length, weight, and amplitude. The period of a simple pendulum can be calculated using a specific equation. Simple pendulums have practical applications in timekeeping, seismology, education, and research.
  • #1
einsteinian
2
0
could you pleassee help me get started on this problem...im not sure how do it

1. A simple pendulum problem of length l oscillates with an amplitude of 45degrees. (Do it without the approx. of sin(theta) = theta)(small angle approx.)

any help would be awesome
 
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  • #2
What do you have to look for?
 
  • #3
wow thanks i can't believe i forgot the most important part...the question

a) period?
b)find the approximate amount of third-harmonic content in the oscillation of the pendulum.
 

1. What is a simple pendulum?

A simple pendulum is a weight suspended from a fixed point by a string or rod. It is an idealized system used to study the behavior of pendulums and is often used in physics experiments.

2. How does a simple pendulum work?

The motion of a simple pendulum is governed by the law of conservation of energy. As the weight swings back and forth, it alternates between potential and kinetic energy. The length of the string and the mass of the weight affect the period, or time it takes for the pendulum to complete one full swing.

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

The period of a simple pendulum is affected by three main factors: the length of the string, the mass of the weight, and the amplitude (angle of swing). A longer string or heavier weight will result in a longer period, while a larger amplitude will result in a shorter period.

4. How is the period of a simple pendulum calculated?

The period of a simple pendulum can be calculated using the following equation: T = 2π√(L/g), where T is the period in seconds, L is the length of the string in meters, and g is the acceleration due to gravity (9.8 m/s²).

5. What are the applications of simple pendulums?

Simple pendulums have many practical applications, such as timekeeping devices (like grandfather clocks), seismometers for measuring earthquakes, and as a tool for demonstrating principles of physics in educational settings. They are also used in research to study oscillatory motion and to measure the effects of gravity.

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