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The motion of a mass on a spring, with s...

The motion of a mass on a spring, with spring constant K is as shown in figure

The equation of motion is given by x(t) `= A sin omegat + B cos omegat ` with `omega=sqrt(K/m)`
Suppose that at time t = 0, the position of mass is x(0) and velocity v (0), then its displacement can also be represented as x(t) = `Ccos(omegat -phi)` , where C and `phi` are :

A

`C=sqrt((2v(0)^2)/(omega^2) +x(0)^(2) ), phi = tan^(-1)((v(0))/(x(0)(omega)))`

B

`C=sqrt((2v(0)^2)/(omega^2) +x(0)^(2) ), phi = tan^(-1)((x(0)omega)/(2v(0)))`

C

`C=sqrt((v(0)^2)/(omega^2) +x(0)^(2) ), phi = tan^(-1)((x(0)omega)/(v(0)))`

D

`C=sqrt((v(0)^2)/(omega^2) +x(0)^(2) ), phi = tan^(-1)((v(0))/(x(0)omega))`

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