Question

In arrangement given in figure, if the block of mass m is displaced, the frequency is given by

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

Answer 1

Answer: (B)

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

Answer 2

With respect to the block the springs are connected in parallel combination.

$\therefore$ Combined stiffness k = k₁+ k₂ and $n = \frac { 1 } { 2 \pi } \sqrt { \frac { k _ { 1 } + k _ { 2 } } { m } }$