# Math Help - Shm :(

1. ## Shm :(

A point moves about O in SHM. The point has velocity v1 at distance x1 and velocity v2 at distance x2. Show that the period of motion is 2 * pi* sqrt[(x1^2-x2^2)/(v2^2-v1^2)].

2. Originally Posted by Sunyata
A point moves about O in SHM. The point has velocity v1 at distance x1 and velocity v2 at distance x2. Show that the period of motion is 2 * pi* sqrt[(x1^2-x2^2)/(v2^2-v1^2)].
hi

$V_1^2=\omega ^2 (X_o^2-X_1^2)$ --- 1

$V_2^2=\omega ^2 (X_o^2-X_2^2)$ ---- 2

2/1 $\frac{V_2^2}{V_1^2}=\frac{X_o^2-X_2^2}{X_o^2-X_1^2}$

$X_o^2=\frac{V_2^2X_1^2-V_1^2X_2^2}{V_2^2-V_1^2}$ --- 3

Substitute into 1

$V_1^2=\omega ^2 (\frac{V_2^2X_1^2-V_1^2X_2^2}{V_2^2-V_1^2}-X_1^2)$

$V_1^2=\omega ^2 (\frac{V_1^2X_1^2-V_1^2X_2^2}{V_2^2-V_1^2})$

$\omega =\frac{2\pi}{T}$

$
T=\sqrt{\frac{4\pi^2(X_1^2-X_2^2)}{V_2^2-V_1^2}}
$