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  4. A tray of mass 12 kg is supported by two identical springs as shown in figure. When the tray is pressed down slightly and then released, it executes SHM with a time period of 1.5 s. The spring constant of each spring is <img class=img-fluid question-image alt=image src=https://cdn.tardigrade.in/img/question/physics/19f0fb723944f9ab55a38d3a479ad074-.png />

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Q. A tray of mass $12 \,kg$ is supported by two identical springs as shown in figure. When the tray is pressed down slightly and then released, it executes SHM with a time period of $1.5\,s$. The spring constant of each spring is
image

KCETKCET 2020Oscillations

Solution:

We know that
$T=2 \pi \sqrt{\frac{m}{k_{\text{eff}}}} $
$\frac{3}{2}=2 \pi \sqrt{\frac{12}{2 k}}$
$ \Rightarrow \frac{9}{4}=4 \pi^{2} \times \frac{12}{2 k} k \approx 105 \,Nm ^{-1}$