Question

A toy car of mass m has 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 car is displaced from the mean position by x cm and released. At the mean position, the ribbons are undeformed. Vibration period is

• A. $2\pi \sqrt{\frac{m\left(2k\right)}{k^2}}$
• B. $\frac{1}{2\pi }\sqrt{\frac{m\left(2k\right)}{k^2}}$
• C. $2\pi \sqrt{\frac{m}{k}}$
• D. $2\pi \sqrt{\frac{m}{k+k}}$

Answer 1

The correct option is C $2\pi \sqrt{\frac{m}{k}}$

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.

$F=kxma=kxa=\frac{kx}{m}a={\omega }^{2}x\omega =\sqrt{\frac{k}{m}}T=\frac{2\pi }{\omega }T=2\pi \sqrt{\frac{m}{k}}$