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

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