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

The motion of a mass on a spring, with spring constant ${K}$ is as shown in figure. The equation of motion is given by $x(t)= A sin \omega t+ Bcos\omega t$ with $\omega=\sqrt{\frac{K}{m}}$ Suppose that at time $t=0$, the position of mass is $x(0)$ and velocity $v(0)$, then its displacement can also be represented as $x(t)=C \cos (\omega t-\phi)$, where $C$ and $\phi$ are

Two masses $m_1$ and $m_2$ connected by a spring of spring constant $k$ rest on a frictionless surface. If the masses are pulled apart and let go, the time period of oscillation is

Two springs, of force constants $k_1$ and $k_2$ are connected to a mass $m$ as shown. The frequency of oscillation of the mass is $f$ If both $k_1$ and $k_2$ are made four times their original values, the frequency of oscillation becomes

A spring block system in horizontal oscillation has a time-period $T$. Now the spring is cut into four equal parts and the block is re-connected with one of the parts. The new time period of vertical oscillation will be

In the situation as shown in figure time period of vertical oscillation of block for small displacements will be