Write equation of relation between time period and frequency.

1.	Write equation of relation between time period and frequency.
Answer» Solution : From graph, initial velocity `= V _(0)` and distance travelled in time `t = X _(0).` For the graph `tan theta = (v_(0))/(x_(0)) = (v _(0) -v)/(x) ""…(1)` Where, v is velocity and x is displacement at any instant of time t. From EQ. (i) `v _(0) -v = (v _(0))/(x_(0)) x` `implies v = (-v _(0))/(x_(0)) x + v _(0) ""...(2)` We know that Acceleration `a = (dv)/(DT) = (- v _(0))/( x _(0)) (dx)/(dt) + 0` `a = (-v_(0))/( x _(0)) (v)` `= (-v _(0))/( x _(0)) ((-v _(0))/( x _(0)) x + v _(0)) (because `From (2)) `= (v _(0) ^(2))/( x _(0) ^(2)) x - ( v _(0) ^(2))/( x _(0))` Graph of a versus x is given above.

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