Question

A block of mass $m$ is suspended by different springs of force constant shown in figure. Let time period of oscillation in these four position be $T_{1}, T_{2}, T_{3}$ and $T_{4}$. Then :

• A. $T_{1}=T_{2}=T_{4}$
• B. $T_{1}=T_{2}$ and $T_{3}=T_{4}$
• C. $T_{1}=T_{2}=T_{3}$
• D. $T_{1}=T_{3}$ and $T_{2}=T_{4}$

Answer 1

Answer: (B)

Time period of oscillations for a spring block system is given by $2 \pi(m / K)^{1 / 2}$ where $K$ is the equivalent force constant of the spring system. Here in first and second figure equivalent force constant is only $k$ whereas in third and foruth figure springs are taken in parallel combination because in both springs deformations are always equal on displacing the block so force constant is $4 k$