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Question

A block of known mass is suspended from a fixed support through a light spring. Can you find the time period of vertical oscillation only by measuring the extension of the spring when the block is in equilibrium?

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Solution

Yes.

Time period of a spring mass system is given by,
T=2πmk ...(1) .
where m is mass of the block, and
k is the spring constant

Time period is also given by the relation,
T=2πx0g ...(2)
where, x0 is extension of the spring, and
g is acceleration due to gravity

From the equations (1) and (2), we have:
mg=kx0

k=mgx0

Substituting the value of k in the above equation, we get:
T=2πmmgx0=2πx0g
Thus, we can find the time period if the value of extension x0 is known.

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