Question

One end of a spring of force constant k is fixed to a vertical wall and the other to a block of mass m resting on a smooth horizontal surface. There is another wall at a distance $x_0$ from the block. The spring is then compressed by $2x_0$ and released. The time taken to strike the wall is

• A.
• B.
• C.
• D.

Answer 1

The correct option is C


The total time from A to C
$=t_{AC}=t_{AB}+t_{BC}=\left(\frac{T}{4}\right)+t_{BC}$
where T = time period of oscillation of spring - mass system
$t_{BC}$ can be obtained from, $BC=AB\sin \left(\frac{2\pi }{T}\right)t_{BC}$
$putting\frac{BC}{AB}=\frac{1}{2}weobtain{t}_{BC}=\frac{T}{12}\Rightarrow t_{AC}=\frac{T}{4}+\frac{T}{12}=\frac{2\pi }{3}\sqrt{\frac{m}{k}}$