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13.Oscillations
medium
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}}}} $
C
$2\pi \sqrt {\frac{m}{k}} $
D
$2\pi \sqrt {\frac{m}{k+k}} $
Solution
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.
$F=k x$
$m a=k x$
$a=\frac{k x}{m}$
$a=\omega^{2} x$
$\omega=\sqrt{\frac{k}{m}}$
$T=\frac{2 \pi}{\omega}$
$T=2 \pi \sqrt{\frac{m}{k}}$
Standard 11
Physics
