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The system shown is lying on a smooth ho...

The system shown is lying on a smooth horizontal surface. Mass `m` is constrained to move along the line `3`. Springs `1` and `2` at right angles with respect to one another are symmetrically arranges with respect to `3` which is an elastic cord. The force constants of `1,2` and `3`are `k` each and they are all just taut in the condition shown. For small oscillations of `m` along `3`, time period is `pisqrt((m)/(yk)) (1+sqrt(x))`. The valye of `xy` is___________

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