Question

A mass $m$ is attached to two springs of same force constant $K$, as shown in following four arrangements. If $T_{1}, T_{2}, T_{3}$ and $T_{4}$ respectively be the time periods of oscillation in the following arrangements, in which case time period is maximum?

• A. a
• B. b
• C. c
• D. d

Answer 1

Answer: (B)

$T=2 \pi \sqrt{\frac{m}{K}}$
Time period is maximum when $K$ is minimum.
In (a), (c) and (d) the spring constants are in parallel so the $K_{ eq }=2 K$.
Only in case (b) springs are in series.
So, $K_{ eq }=\frac{K}{2}$
Hence time period in this case will be maximum.