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tataratat
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Having recently completed a session on the simple pendulum in physics, I was curious as to what the solution to θ''+(g/l)sin(θ)=0 for θ(t) was sans the sin(θ)=θ simplification.
sweet springs said:θ''+(g/l)sin(θ)=0
Multiply [tex]\theta^.[/tex] to make [tex]{{\theta^.}^2}^. [/tex], integrate and then take square root to get [tex]\frac{dt}{d\theta}[/tex]
A simple pendulum is a theoretical model consisting of a point mass suspended by a weightless and rigid string or rod. It is used to study the effects of gravity and oscillatory motion.
The equation of motion for a simple pendulum is given by T = 2π√(l/g), where T is the period (time for one complete oscillation), l is the length of the pendulum, and g is the acceleration due to gravity.
The length of the pendulum directly affects its period of oscillation. A longer pendulum will have a longer period, while a shorter pendulum will have a shorter period. This is because a longer pendulum has a greater distance to travel in one oscillation, resulting in a longer time period.
The motion of a simple pendulum is affected by the length of the pendulum, the mass of the pendulum, the amplitude of the oscillation, and the strength of gravity. Friction and air resistance can also play a role in the motion of a pendulum.
A simple pendulum is used in scientific experiments to demonstrate the principles of oscillatory motion and to measure the effects of gravity. It is also used to study the effects of different variables, such as length and mass, on the motion of the pendulum. In addition, the simple pendulum is often used as a timing device in experiments, as its period is constant for a given length and mass.