Question

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

• A. $50 \,Nm^{-1}$
• B. $0$
• C. $105 \,Nm^{- 1}$
• D. $\infty$

Answer 1

Answer: (C)

$105 \,Nm^{- 1}$

Answer 2

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