Is Amplitude REALLY independent from Period and Frequency??

[libraryismyhome]

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Many BR questions were saying that Amplitude is independent from Period and Frequency in periodic motion.

So we all know that for a spring equation, x is the amplitude
PE of Spring = (1/2)kx^2

However, since this PE of spring could be easily converted to kinetic energy which is

PE of Spring = (1/2)kx^2 = (1/2)mv^2 = Kinetic Energy

So, we can find out the maximum velocity and maximum acceleration. Does this mean that we can find out the Period(time it takes to complete one periodic motion) and the frequency as well?


Though not a periodic motion, there is a sound intensity equation as well.
Intensity = (1/2)f^2 A^2 v d
Because of this equation, how is Amplitude completely independent of frequency or period??

 

[RogueUnicorn]

i don't see why the intensity equation somehow makes amplitude dependent on f or T? independent variables can appear in the same equation.

let's go back to the spring. whether you pull the spring WAAAYYY far out, or very little out, it will complete the cycle over the same period. naturally, the former scenario also carries higher speed, but that's because it has to cover a greater distance, leaving the time unchanged.

you can see this for yourself by a makeshift pendulum.

 

[libraryismyhome]

let's go back to the spring. whether you pull the spring WAAAYYY far out, or very little out, it will complete the cycle over the same period. naturally, the former scenario also carries higher speed, but that's because it has to cover a greater distance, leaving the time unchanged.

oh yeah right!!!! 😀