Continuare de aici: http://brainly.ro/tema/252211 (ca sa nu fie confuzii)
[tex]\dfrac{x_0}{A}=\sqrt{1-\dfrac{v_0^2}{\omega^2A^2}}\\ \\ \\ \dfrac{x_0^2}{A^2}=1-\dfrac{v_0^2}{\omega^2A^2}\\ \\ \\ \dfrac{x_0^2}{A^2}+\dfrac{v_0^2}{\omega^2A^2}=1\\ \\ \\ \dfrac{\omega^2 x_0^2+v_0^2}{\omega^2A^2}=1\\ \\ \\ \omega^2A^2=\omega^2 x_0^2+v_0^2[/tex]
Se putea si mai rapid, dar asta e ideea generala. Acum, l-am izolat pe A intr-o parte, mai ramane doar sa scap si de omega patrat:
[tex]A^2=\dfrac{\omega^2 x_0^2+v_0^2}{\omega^2}\\ \\ \\ A^2=x_0^2+\dfrac{v_0^2}{\omega^2}\\ \\ \\ A=\sqrt{x_0^2+\dfrac{v_0^2}{\omega^2}}[/tex]
Gata!
