$A$ spring with a force constant $180 \text{ N/m}$ is loaded with a mass $0.2 \text{ kg}$. The amplitude of oscillations is $4 \text{ cm}$. When the mass comes to the equilibrium position, its velocity is: (in $\text{ m/s}$)

$A$ 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 $N$?

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

Two identical springs of spring constant $2k$ are attached to a block of mass $m$ and to fixed supports (see figure). When the mass is displaced from the equilibrium position on either side,it executes simple harmonic motion. The time period of oscillations of this system is ...... .

$A$ flat horizontal board moves up and down in $S.H.M.$ vertically with amplitude $A$. The shortest permissible time period of the vibration such that an object placed on the board may not lose contact with the board is ..........

$A$ $10 \,kg$ metal block is attached to a spring of spring constant $1000 \,N \,m^{-1}$. The block is displaced from the equilibrium position by $10 \,cm$ and released. The maximum acceleration of the block is: (in $\,m/s^2$)