$A$ tray of mass $12 \,kg$ is supported by two identical springs as shown in the 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

$A$ mass of $0.2\,kg$ is attached to the lower end of a massless spring of force-constant $200\,N/m,$ the upper end of which is fixed to a rigid support. Which of the following statements is/are true?

Two springs with force constants $k_1$ and $k_2$ have the same mass attached to their ends. Both objects have the same maximum velocity. What is the ratio of their amplitudes?

If a spring has time period $T$,and is cut into $n$ equal parts,then the time period of each part will be

The time period of simple harmonic motion of mass $M$ in the given figure is $\pi \sqrt{\frac{\alpha M}{5 K}}$,where the value of $\alpha$ is . . . . . . .

$A$ highly rigid cubical block $A$ of small mass $M$ and side $L$ is fixed rigidly onto another cubical block $B$ of the same dimensions and of low modulus of rigidity $\eta$ such that the lower face of $A$ completely covers the upper face of $B$. The lower face of $B$ is rigidly held on a horizontal surface. $A$ small force $F$ is applied perpendicular to one of the side faces of $A$. After the force is withdrawn,block $A$ executes small oscillations. The time period of which is given by: