Question

A block of mass m compresses a spring of stiffness k through a distance (/2) as shown in the figure. If the block is not connected with the spring and the impact of the block with the vertical wall is elastic, the period of motion of the block is

• A. 2π$\sqrt { \frac { m } { k } }$
• B. (π + 4) $\sqrt { \frac { m } { k } }$
• C. (1 + π)$\sqrt { \frac { m } { k } }$
• D. None of these.

Answer 1

Answer: (B)

(π + 4) $\sqrt { \frac { m } { k } }$

Answer 2

The period of oscillation = 2π

⇒ The period of motion till the block is in contact with the spring

t₁ = π then it leaves the spring with a speed v = ωA

v =

Then it moves with constant velocity v for a distance D = + = 2 ⇒ The corresponding time of motion = t₂ = 2/v

⇒ t₂ = $\frac { 2 \ell } { \frac { \ell } { 2 } \sqrt { \frac { k } { m } } } = 4 \sqrt { \frac { \mathrm { m } } { \mathrm { k } } }$ ∴ The time period of motion

= t = ₁ + t₂ = π + 4 = [ π + 4].

Hence Answer is (B).