NEET-XII-Physics
12: Simple Harmonic Motion
- #14A 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?Ans : 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:
`` T=2\pi \sqrt{\frac{m}{{\displaystyle \frac{mg}{{x}_{0}}}}}=2\,\mathrm{\,\pi \,}\sqrt{\frac{{\,\mathrm{\,x\,}}_{0}}{\,\mathrm{\,g\,}}}``
Thus, we can find the time period if the value of extension x0 is known.
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