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13.Oscillations
easy
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
$(d)$
Solution
(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, $K_{\text {eq }}=\frac{K}{2}$
Hence time period in this case will be maximum.
Standard 11
Physics
