Amplitude calculation

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July 25th 2012, 05:31 AM
Neverquit

Amplitude calculation

How can I solve for Amplitude and Period if I have the following data?
a=-4^2.x (ie. SHM)

x = 2m, speed = sqrt(10 )m/s

given I cannot use k=4 from a=-4^2.x

I was thinking to use v^2=k^2(A^2-x^2)

so 10=k^2(A^2-4) but then I have 2 unknowns?
July 25th 2012, 06:26 AM
ebaines

Re: Amplitude calculation

For simple harmonic motion

$x = A \sin(\omega t)$ ,

$v = \frac {dx}{dt} = A \omega \cos(\omega t) = \omega \sqrt{A^2-x^2}$ ,

$a = \frac {d^2x}{dt^2} = -A \omega \sin(\omega t) = -\omega^2 x$

From the acceleration equation if you are given that $a = -4^2 x$ then $\omega = 4 s^{-1}$ .

If $v = \sqrt{10}$ at x = 2m, then from the velocity equation:

$\sqrt{10} = 4 \sqrt{A^2 - 2^2$
$A = \frac {\sqrt {74}} {4} m$

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