$A, B, C$ are identical springs each of spring constant $k$ as shown in figure. Mass $M$ is displaced slightly along $C$ and released. Find the time period of small oscillation.

T = 2 π \sqrt{\frac{m}{k}}

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T = 2 π \sqrt{\frac{2 m}{2 k}}

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T = 2 π \sqrt{\frac{m}{2 k}}

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T = 2 π \sqrt{\frac{3 m}{2 k}}

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Solution

The correct option is C $T = 2 π \sqrt{\frac{m}{2 k}}$
Net force as shown in figure is $F = - (k x + k x cos 60 + k x cos 60) = - 2 k x$
$m a = - 2 k x$
or $a = \frac{- 2 k}{m} x$
On comparing with a = - $ω^{2} x$
$ω = \sqrt{\frac{2 k}{m}}$
or $T = 2 π \sqrt{\frac{m}{2 k}}$

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A,B,C are identical springs each of spring constant k as shown in figure. Mass M is displaced slightly along C and released. Find the time period of small oscillation.

The correct option is C T=2π√m2kNet force as shown in figure is F=−(kx+kxcos60+kxcos60)=−2kxma=−2kxor a=−2kmxOn comparing with a = -ω2xω=√2kmor T=2π√m2k

$A, B, C$ are identical springs each of spring constant $k$ as shown in figure. Mass $M$ is displaced slightly along $C$ and released. Find the time period of small oscillation.

The correct option is C $T = 2 π \sqrt{\frac{m}{2 k}}$
Net force as shown in figure is $F = - (k x + k x cos 60 + k x cos 60) = - 2 k x$
$m a = - 2 k x$
or $a = \frac{- 2 k}{m} x$
On comparing with a = - $ω^{2} x$
$ω = \sqrt{\frac{2 k}{m}}$
or $T = 2 π \sqrt{\frac{m}{2 k}}$