Question

One end of a spring of force constant \(k\) is fixed to a wall and other end is connected to a block of mass \(m\) resting on a smooth horizontal surface as shown. The spring is now compressed by \(3l\) and released, the time after which the block will strike the other wall is


4 isidis \( m \) in

• A. $[\pi -{\sin }^{-1}\left(\frac{1}{3}\right)]\sqrt{\frac{m}{k}}$
• B. $[\pi -{\cos }^{-1}\left(\frac{1}{3}\right)]\sqrt{\frac{m}{k}}$
• C. ${\sin }^{-1}\left(\frac{1}{3}\right)\sqrt{\frac{m}{k}}$
• D. $\pi \sqrt{\frac{m}{k}}$

Answer 1

The correct option is B $[\pi -{\cos }^{-1}\left(\frac{1}{3}\right)]\sqrt{\frac{m}{k}}$

$\omega =\sqrt{\frac{k}{m}}$
$\omega t=(\frac{\pi }{2}+si{n}^{-1}\frac{1}{3})$
$t=\frac{\pi -{\cos }^{-1}\left(\frac{1}{3}\right)}{\omega }$