A block of mass m is having two similar rubber ribbons attached t… - Vidyadip

MCQ

A block of mass $m$ is having two similar rubber ribbons attached to it as shown in the figure. The force constant of each rubber ribbon is $K$ and surface is frictionless. The block is displaced from mean position by $x\,cm$ and released. At the mean position the ribbons are underformed. Vibration period is

A
$2\pi \sqrt {\frac{{m(2k)}}{{{k^2}}}} $
B
$\frac{1}{{2\pi }}\sqrt {\frac{{m(2k)}}{{{k^2}}}} $
✓
$2\pi \sqrt {\frac{m}{k}} $
D
$2\pi \sqrt {\frac{m}{k+k}} $

✓

Answer

Correct option: C.

$2\pi \sqrt {\frac{m}{k}} $

c
Displace the car by distance $x,$ one of the rubber will get stretched by $x$ but another will loose to apply any force as rubber cant be compressed like spring.

$F=k x$

$m a=k x$

$a=\frac{k x}{m}$

$a=\omega^{2} x$

$\omega=\sqrt{\frac{k}{m}}$

$T=\frac{2 \pi}{\omega}$

$T=2 \pi \sqrt{\frac{m}{k}}$

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