$A$ particle of mass $m$ is attached to three identical massless springs of spring constant $k$ as shown in the figure. The time period of vertical oscillation of the particle is

If $A$ is the area of cross-section of a spring,$L$ is its length,$E$ is the Young's modulus of the material of the spring,then the time period and force constant of the spring will be respectively:

$A$ body of mass $m$ is attached to a spring which is oscillating with time period $6 \ s$. If the mass of the body is increased by $6 \ kg$,its time period increases by $3 \ s$. Determine the initial mass $m$. (in $kg$)

One end of a spring of force constant $k$ is fixed to a vertical wall and the other to a block of mass $m$ resting on a smooth horizontal surface. There is another wall at a distance $x_0$ from the block. The spring is then compressed by $2x_0$ and released. The time taken to strike the wall is

Two masses $m_1 = 1 \, kg$ and $m_2 = 0.5 \, kg$ are suspended together by a massless spring of spring constant $k = 12.5 \, N/m$. When the masses are in equilibrium,$m_1$ is removed without disturbing the system. The new amplitude of oscillation will be .......... $cm$.

$A$ block $P$ of mass $m$ is placed on a frictionless horizontal surface. Another block $Q$ of the same mass $m$ is kept on $P$ and connected to a wall with the help of a spring of spring constant $k$ as shown in the figure. $\mu_s$ is the coefficient of static friction between $P$ and $Q$. The blocks move together performing simple harmonic motion $(SHM)$ of amplitude $A$. The maximum value of the friction force between $P$ and $Q$ is