A particle executing harmonic motion is having velocities `v_1` and `v_2` at distances is `x_1` and `x_2` from the equilibrium position. The amplitude of the motion is

Options

A. `sqrt((v_1^2+x_2-v_2^2x_1)/(v_1^2-v_2^2))`
B. `sqrt((v_1^2x_1^2-v_2^2x_2^2)/(v_1^2+v_2^2))`
C. `sqrt((v_1^2x_2^2-v_2^2x_1^2)/(v_1^2-v_2^2))`
D. `sqrt((v_1^2x_2^2+v_2^2x_1^2)/(v_1^2+v_2^2))`

Answer

C

Explanation

`v_1=omegasqrt(a^2-x_1^2)`,`v_2=sqrt(a^2-x_2^2)`
We get `a=sqrt((v_1^2x_2^2-v_2^2x_1^2)/(v_1^2-v_2^2))`