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13.Oscillations
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અવગણ્ય દળ ધરાવતી સ્પ્રિંગથી લટકાવેલ $M$ દળનો આવર્તકાળ $T$ છે. હવે તેની સાથે બીજુ $M$ દળ લટકાવતા હવે, દોલનનો આવર્તકાળ કેટલો થાય?
A
$T$
B
$\frac{T}{{\sqrt 2 }}$
C
$2T$
D
$\sqrt 2 $$T$
(AIPMT-2010)
Solution

A mass $M$ is suspended from a massless spring of spring constant $k$ as shown in figure $(a)$. Then,
Time period of oscillation is
$T=2 \pi \sqrt{\frac{M}{k}}$
When a another mass $M$ is also suspended with it as shown in figure $(b).$
Then,
Time period of oscillation is
$T^{\prime} =2 \pi \sqrt{\frac{M+M}{k}}=2 \pi \sqrt{\frac{2 M}{k}}$
$=\sqrt{2}(2 \pi \sqrt{\frac{M}{k}})=\sqrt{2} T \quad(\text { Using }(\mathrm{i}))$
Standard 11
Physics