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A particle is executing simple harmonic motion along a straight line. At displacements $r_1 \: and r_2$ from its mean position the velocities are $v_1 \: and \: v_2$ . The time period of the particle is

$\begin {array} {1 1} (1)\;2 \pi \bigg[ \large\frac{r_2^2-r_1^2}{v_2^2-v_1^2}\bigg]^{\large\frac{1}{2}} & \quad (2)\;2 \pi \bigg[ \large\frac{v_1^2 - v_2^2}{r_2^2+r_1^2} \bigg]^{\large\frac{1}{2}} \\ (3)\;\large\frac{1}{2 \pi } \bigg[ \large\frac{v_1^2+v_2^2}{r_2^2-r_1^2} \bigg]^{\large\frac{1}{2}} & \quad (4)\;2 \pi \bigg[ \large\frac{r_2^2-r_1^2}{v_1^2-v_2^2} \bigg]^{\large\frac{1}{2}} \end {array}$

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(4) $ 2 \pi \bigg[ \large\frac{r_2^2-r_1^2}{v_1^2-v_2^2} \bigg]^{\large\frac{1}{2}}$
answered Nov 7, 2013 by pady_1

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