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,
(Consider springs to be massless.)

• A. $T_1=T_2=T_4$
• B. $T_1=T_2\text{and}{T}_3=T_4$
• C. $T_1=T_2=T_3$
• D. $T_1=T_3\text{and}{T}_2=T_4$

Answer 1

The correct option is B $T_1=T_2\text{and}{T}_3=T_4$

Time period of oscillations for a spring block system is given by $2\pi \sqrt{\frac{m}{K}}$
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 fourth figure springs are taken in parallel combination because in both springs deformations are always equal on displacing the block so force constant is $4K$.
Hence, option (B) is correct.