$A$ spring with a spring constant of $1200\, Nm^{-1}$ is mounted on a smooth frictionless surface and attached to a block of mass $3\, kg$. The block is pulled $2\, cm$ to the right and released. The angular frequency of oscillation is .... $rad/s$.

Two identical springs of spring constant $k$ are attached to a block of mass $m$ and to fixed supports as shown in the figure. When the mass is displaced from the equilibrium position by a distance $x$ towards the right,find the restoring force.

$A$ mass $M$ is suspended by two springs of force constants $K_1$ and $K_2$ respectively,as shown in the diagram. The total elongation (stretch) of the two springs is

When the mass attached to a spring is increased from $4 \ kg$ to $9 \ kg$,the time period of oscillation increases by $0.2 \pi \ s$. Then the spring constant of the spring is (in $N \ m^{-1}$)

The total mechanical energy of a spring-mass system in simple harmonic motion is $E = \frac{1}{2}m\omega^2 A^2$. Suppose the oscillating particle is replaced by another particle of double the mass while the amplitude $A$ remains the same. The new mechanical energy will:

$A$ force of $6.4 \ N$ stretches a vertical spring by $0.1 \ m$. The mass that must be suspended from the spring so that it oscillates with a time period of $\pi/4 \ s$ is .... $kg$.