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?
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?
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 $
$\displaystyle A = \frac {\sqrt {74}} {4} m$