If your heart is beating at 76 beats per minute what is the frequency of your heart's oscillations

Physics

1 answer:

PSYCHO15rus [73]3 years ago

4 0

That would be a frequency of 1.2666... beats per second. This can be phrased as your heart beats at 1.27 Hz.

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$0=-a\sin(wt)+w\cos(wt)\iff a\sin(wt)=w\cos(wt)\iff \\\\\sin(wt)=\dfrac{w}{a}\cos(wt)\iff \tan(wt)=\dfrac{w}{a}\iff wt=\tan^{-1}\left(\dfrac{w}{a}\right)\iff \\\\\boxed{t=\dfrac{1}{w}\tan^{-1}\left(\dfrac{w}{a}\right)}$

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Hence:

$T(t)=\dfrac{5w}{\sqrt{w^2+a^2}}e^{-\frac{a}{w}\tan^{-1}\left(\frac{w}{a}\right)}$

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