In the video, it was remarked that for small values of the equation of motion for the pendulum, 9 sin 0 = 0 is similar to the linear spring equation. If we take two nonzero terms of the L series for sin into account, the model is even more spring-like, but this time to a non-linear spring. From this perspective, which of the following kind of spring is the pendulum most like?
O ideal linear spring
O hard spring O soft spring

They swing back and forth around a stationary point. Classic examples of this type of vibrating motion are a simple pendulum and a mass on a spring. The use of motion detectors demonstrates that the vibrations of these items have a sinusoidal character, even if this is not obvious from plain viewing.

Let θ be A,

[tex]A''+(g/l)sinA=0\\sinA=A - (A^{3} /3!)+(A^{5} /5!)....\\[/tex]

taking first 2 terms,

[tex]A'' +(g/l)(A-A^{3}/3!)\\[/tex]

intergrating both sides,

[tex]A'+(g/l)(A^{2}/2 -A^{4}/24)=c[/tex]

integrating again,

[tex]A+(g/l)(A^{3} /6-A^{5}/120)=ct+c_{1}[/tex]

power is 5= non linear spring

Additionally, a larger degree indicates that the displacement over time diminishes more quickly.

Hence its a hard spring.

To know more about spring checkout https://brainly.com/question/14670501

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