$A$ particle of mass $0.50 \ kg$ executes simple harmonic motion under force $F = -50 \ (N/m) x$. The time period of oscillation is $\frac{x}{35} \ s$. The value of $x$ is . . . . . (Given $\pi = \frac{22}{7}$)

$A$ 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 $M$ attached to a horizontal spring executes simple harmonic motion with amplitude $A_1$. When mass $M$ passes the mean position,a smaller mass $m$ is attached to it,and both of them together execute simple harmonic motion with amplitude $A_2$. Then the value of $\frac{A_1}{A_2}$ is

If the period of oscillation of mass $m$ suspended from a spring is $2 \ s$,then the period of oscillation of suspended mass $4m$ with the same spring will be: (in $s$)

The potential energy of a particle of mass $100 \,g$ moving along the $x$-axis is given by $U = 5x(x - 4)$,where $x$ is in metres. The period of oscillation is .................

$A$ block is placed on a frictionless horizontal table. The mass of the block is $m$ and springs are attached on either side with force constants $K_1$ and $K_2$. If the block is displaced a little and left to oscillate,then the angular frequency of oscillation will be