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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,\[T = 2\pi\sqrt{\frac{m}{k}}\] ...(1) where m is mass of the block, and
k is the spring constant
Time period is also given by the relation,
\[T = 2\pi\sqrt{\frac{x_0}{g}}\] ...(2)
where, x0 is extension of the spring, and
g is acceleration due to gravity
From the equations (1) and (2), we have :
\[mg = k x_0\]
\[\Rightarrow k = \frac{mg}{x_0}\]
Substituting the value of k in the above equation, we get:
Thus, we can find the time period if the value of extension x0 is known.
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