# Amplitude calculation

• Jul 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?
• Jul 25th 2012, 06:26 AM
ebaines
Re: Amplitude calculation
For simple harmonic motion

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

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

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

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

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

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