Question

A mass m is suspended by means of two coiled spring which have the same length in unstretched condition as in figure. Their force constant are k₁ and k₂ respectively. When set into vertical vibrations, the period will be

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

Answer 1

Answer: (D)

$2 \pi \sqrt { \left( \frac { m } { k _ { 1 } + k _ { 2 } } \right) }$

Answer 2

Given spring system has parallel combination, so

$k _ { e q } = k _ { 1 } + k _ { 2 }$ and time period $T = 2 \pi \sqrt { \frac { m } { \left( k _ { 1 } + k _ { 2 } \right) } }$