Question

One end of a spring of force constant k is fixed to a vertical wall and the other to body of mass m resting on a smooth horizontal surface. There is another wall at a distance x₀ from the body. The spring is then compressed by 2x₀ and released. The time taken to strike the wall first time is –

• A.
• B. $\sqrt { \frac { \mathrm { m } } { \mathrm { k } } }$
• C. $\frac { 2 \pi } { 3 } \sqrt { \frac { \mathrm {~m} } { \mathrm { k } } }$
• D.

Answer 1

Answer: (C)

$\frac { 2 \pi } { 3 } \sqrt { \frac { \mathrm {~m} } { \mathrm { k } } }$

Answer 2

The total time from A to C

t_AC = t_AB + t_BC = + t_BC

Where T = Time period of oscillation of spring-mass system t_BC can be given by

BC = AB sin t_BC

Putting $\frac { 1 } { 2 }$, we get

t_BC =

\ t_BC = $\frac { 2 \pi } { 3 } \sqrt { \frac { \mathrm {~m} } { \mathrm { k } } }$