$2222.$ A platform, having an unknown mass, is supported by four springs, each having the same stiffness

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$.$ When nothing is on the platform, the period of vertical vibration is measured as $2\mathrm{.}35$ s; whereas if a

$3$

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kg

block is supported on the platform, the period of vertical vibration is $5\mathrm{.}23$ s$.$ Determine the mass of a block placed on the $($empty$)$ platform which causes the platform to vibrate vertically with a period of $5\mathrm{.}62$ s$.$ What is the stiffness

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of each of the springs?