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The most accurate way to model a pendulum (without air resistance) is as a differential equation in terms of the angle it makes with the vertical, θ, the length of the pendulum, l, and the acceleration due to gravity, g.
d²θ/dt² = -g*sin(θ)/l
There is no easy way to integrate this to get θ as a function of time, but if you assume θ is small, you can use the small angle approximation sin(θ)~θ which makes the equation
d²θ/dt² = -g*θ/l
Which can then be integrated to get the solution
θ(t)=θmax*sin(t*√(g/l))
Using this equation, you can easily derive that the period of the pendulum (time required to go through one full cycle) would be
T=2π*√(l/g)
If air resistance is also accounted for in the original differential equation, the exact equation will be much harder to derive, but in general will involve an exponential decay of a sin function.
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∙ 14y ago
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The angle between the string of a pendulum at its equilibrium position and at its maximum displacement is the pendulums?
amplitude
How is a pendulum used in the world today?
Pendulums are often used in clocks to power the gears that move the hands. However, most clocks built today often have pendulums only for show, as those types of clocks are usually inaccurate and require a lot of winding.
What is the period of the pendulum?
The period of a simple pendulum, with very short swings, is approximated byT = 2 pi (L/G)(0.5)More complex pendulums, or pendulums with greater than insignificant swing, have more complex equations, usually to correct for circular error.
How is inertia related to pendulums?
Inertia is a massive object's resistance to change. It should be obvious then that mass is directly proportional to how long the pendulum swings before coming to rest, since more mass means harder to stop. Mathematically, you'll find this dependence on mass in the damping equations of pendulums.
Does a short or a long pendulum have a longer period?
The time of swing of a pendulum is T = 2π √ (l/g) where l is the length of the pendulum. As T ∝√l (Time is directly proportional to the square root of l) then, the longer the pendulum, the greater is the period. Therefore longer pendulums have longer periods than shorter pendulums.
What are different types of pendulum?
Some common types of pendulums include simple pendulums, compound pendulums, physical pendulums, and torsion pendulums. Simple pendulums consist of a mass suspended from a fixed point and swing back and forth. Compound pendulums have multiple arms or masses swinging together. Physical pendulums have a mass distributed along its length instead of at a single point. Torsion pendulums use a twisting motion instead of swinging back and forth.
What is the plural of pendulum?
The plural of pendulum is pendulums.
What is a swinging pendulum?
All pendulums swing. They wouldn't be pendulums if they didn't.
Are pendulums and the spirits they invoke evil?
no pendulums are not used for evil or tp provoke evil spirits pendulums are fastinating but are used for questions or any other way you can think of .
How many different types of pendulums are there?
There are two main types of pendulums: simple pendulums, which consist of a mass (bob) attached to a string or rod swinging back and forth, and compound pendulums, which have multiple bobs or arms that can oscillate independently. Within these two categories, there can be various designs and configurations for pendulums used in different applications.
What are some pendulums?
That one.
What is a Pendulum Toy?
pendulums
What tools are used to time?
There are several tools used to tell time. These tools include wristwatches, digital clocks, analog clocks, sundials, pendulums, chronometers, equation clocks, and obelisks.
Where can you find pendulums?
Pendulums can be found in specialty stores that sell spiritual or metaphysical items, online retailers, or at local craft stores. Etsy and Amazon are popular online platforms where you can find a variety of pendulums for sale.
What if you pull two pendulums of opposite ends from newtons cradle?
If you pull two pendulums of opposite ends from a Newton's cradle, the energy will transfer through the remaining pendulums in the system. The motion created will depend on the relative masses and lengths of the pendulums involved, leading to a complex interplay of energy transference and motion.
What tools are used to tell time?
There are several tools used to tell time. These tools include wristwatches, digital clocks, analog clocks, sundials, pendulums, chronometers, equation clocks, and obelisks.
Why are all Pendulums the same?
because of same length
