Question

Two identical springs of constant k are connected in series and parallel as shown in figure. A mass m is suspended from them. The ratio of their frequencies of vertical oscillation will be

• A. 2 : 1
• B. 1 : 1
• C. 1 : 2
• D. 4 : 1

Answer 1

Answer: (C)

1 : 2

Answer 2

For series combination $n _ { 1 } \propto \sqrt { k / 2 }$

For parallel combination $n _ { 2 } \propto \sqrt { 2 k }$ so $\frac { n _ { 1 } } { n _ { 2 } } = \sqrt { \frac { k / 2 } { 2 k } } = \frac { 1 } { 2 }$ .