Question

In the figure, $S _ { 1 }$ and $S _ { 2 }$ are identical springs. The oscillation frequency of the mass m is $f$. If one spring is removed, the frequency will become

• A. $f$
• B. $f \times 2$
• C. $f \times \sqrt { 2 }$
• D. $f / \sqrt { 2 }$

Answer 1

Answer: (D)

$f / \sqrt { 2 }$

Answer 2

For the given figure $f = \frac { 1 } { 2 \pi } \sqrt { \frac { k _ { e q } } { m } } = \frac { 1 } { 2 \pi } \sqrt { \frac { 2 k } { m } }$ …..(i)

If one spring is removed, then k_eq = k and $f ^ { \prime } = \frac { 1 } { 2 \pi } \sqrt { \frac { k } { m } }$ ….(ii)

From equation (i) and (ii), $f ^ { \prime } = \frac { f } { \sqrt { 2 } }$