A mass m is attached to two springs of same force constant K , as shown in following four arrangemen

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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?

$(a)$

$(b)$

$(c)$

$(d)$

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

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(AIPMT-2004)

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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?

Solution

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