A spring compressed by $0.1 \mathrm{m}$ develops a restoring force $10 \mathrm{N}$. Deduce the force constant $k$ of the spring.

A spring compressed by $0.1 \mathrm{m}$ Develops a restoring force $10 \mathrm{N}$. A body of mass $4 \mathrm{kg}$ is placed on it. Deduce the depression of the spring under the weight of the body. (take $g=10 \raisebox{1ex}{${\displaystyle \mathrm{N}}$}\!\left/ \!\raisebox{-1ex}{$\mathrm{kg}$}\right.$)

A spring compressed by $0.1 \mathrm{m}$ develops a restoring force $10 \mathrm{N}$. A body of mass $4 \mathrm{kg}$ is placed on it. Deduce the period of oscillation, if the body is disturbed.

A mass $M$ is attached to a spring which oscillates with a period of $2 \mathrm{s}$. If the mass is increased by $2 \mathrm{kg}$, the period increased by $1 \mathrm{s}$. Find the initial mass $M$, assuming that Hooke’s law is obeyed.

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