The force constant of a weightless spring is $16 \, N/m$. $A$ body of mass $1.0 \, kg$ suspended from it is pulled down through $5 \, cm$ and then released. The maximum kinetic energy of the system (spring + body) will be

Two masses $m_1$ and $m_2$ are suspended together by a massless spring of constant $k$. When the masses are in equilibrium,$m_1$ is removed without disturbing the system. Then the angular frequency of oscillation of $m_2$ is

Consider two identical springs each of spring constant $k$ and negligible mass compared to the mass $M$ as shown. Fig. $1$ shows one of them and Fig. $2$ shows their series combination. The ratio of the time period of oscillation of the two $SHM$ is $\frac{T_b}{T_a} = \sqrt{x}$,where the value of $x$ is (Round off to the Nearest Integer).

When a mass $m$ is attached to a spring,it normally extends by $0.2\, m$. If the mass $m$ is given a slight additional extension and released,what will be its time period?

Two identical springs of spring constant $k$ are attached to a block of mass $m$ and to fixed supports as shown in the figure. Show that when the mass is displaced from its equilibrium position on either side,it executes simple harmonic motion. Find the period of oscillations.

$A$ block with mass $M$ is connected by a massless spring with stiffness constant $k$ to a rigid wall and moves without friction on a horizontal surface. The block oscillates with small amplitude $A$ about an equilibrium position $x_0$. Consider two cases: $(i)$ when the block is at $x_0$; and $(ii)$ when the block is at $x = x_0 + A$. In both cases, a particle with mass $m$ is placed on the mass $M$. Which of the following statements are correct?