Question

A mass m is suspended from the two coupled springs connected in series. The force constant for springs are $K _ { 1 }$ and $K _ { 2 }$ . The time period of the suspended mass will be

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

Answer 1

Answer: (C)

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

Answer 2

In series $k _ { e q } = \frac { k _ { 1 } k _ { 2 } } { k _ { 1 } + k _ { 2 } }$so time period

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