Springs of spring constants $K, 2K, 4K, 8K, \dots$ are connected in series. $A$ mass of $40 \, g$ is attached to the lower end of the last spring and the system is allowed to vibrate. What is the time period of oscillation in seconds? (Given $K = 2 \, N/cm$)

$A$ spring balance has a scale that reads from $0$ to $50\; kg$. The length of the scale is $20\; cm$. $A$ body suspended from this balance,when displaced and released,oscillates with a period of $0.6\; s$. What is the weight of the body in $N$?

When a particle of mass $m$ is attached to a vertical spring of spring constant $k$ and released,its motion is described by $y(t) = y_{0} \sin^{2} \omega t$,where $y$ is measured from the lower end of the unstretched spring. Then $\omega$ is

All the springs in figures $(a)$,$(b)$,and $(c)$ are identical,each having a force constant $K$. $A$ mass $m$ is attached to each system. If $T_a, T_b$,and $T_c$ are the time periods of oscillations of the three systems in figures $(a)$,$(b)$,and $(c)$ respectively,then:

$A$ simple harmonic oscillator consists of a particle of mass $m$ and an ideal spring with spring constant $k$. The particle oscillates with a time period $T$. The spring is cut into two equal parts. If one part oscillates with the same particle, the new time period will be

$A$ 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 After the force is withdrawn,block $A$ executes small oscillations.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: