Department of Pre-University Education, KarnatakaPUC Karnataka Science Class 11
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A Block of Known Mass is Suspended from a Fixed Support Through a Light Spring. Can You Find the Time Period of Vertical Oscillation - Physics

Short Note

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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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
            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:

\[T = 2\pi\sqrt{\frac{m}{\frac{mg}{x_0}}} = 2\pi\sqrt{\frac{x_0}{g}}\]

Thus, we can find the time period if the value of extension x0 is known.

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HC Verma Class 11, 12 Concepts of Physics 1
Chapter 12 Simple Harmonics Motion
Short Answers | Q 14 | Page 250
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