A block whose mass is $1 \mathrm{kg}$ is fastened to a spring. The spring has a spring constant of $50 {\mathrm{Nm}}^{-1}$. The block is pulled to a distance $x=10 \mathrm{cm}$ from its equilibrium position at $x=0$ and a frictionless surface from rest at $t=0$. Calculate the kinetic, potential and total energies of the block when it is $5 \mathrm{cm}$ away from the mean position.

A spring balance has a scale that reads from $0$ to $50 \mathrm{kg}$. The length of the scale is $20 \mathrm{cm}$. A body suspended from this spring, when displaced and released, oscillates with a period of $0.6 \mathrm{s}$. What is the weight of the body?

A spring of force constant $1200 {\mathrm{Nm}}^{-1}$ is mounted on a horizontal table as shown in [Fig. 22.581. A mass of $3.00 \mathrm{kg}$ is attached to the free end of the spring, pulled sideways to a distance of $2.0 \mathrm{cm}$ and released.

What is the frequency of oscillation of the mass?

A spring of force constant $1200 {\mathrm{Nm}}^{-1}$ is mounted on a horizontal table as shown in [Fig. 22.581. A mass of $3.00 \mathrm{kg}$ is attached to the free end of the spring, pulled sideways to a distance of $2.0 \mathrm{cm}$ and released.

What is the maximum acceleration of the mass?

A spring of force constant $1200 {\mathrm{Nm}}^{-1}$ is mounted on a horizontal table as shown in [Fig. 22.581. A mass of $3.00 \mathrm{kg}$ is attached to the free end of the spring, pulled sideways to a distance of $2.0 \mathrm{cm}$ and released.

What is the maximum speed of the mass?

A body of mass $12 \mathrm{kg}$ is suspended by a coiled spring of natural length $50 \mathrm{cm}$ and force constant $2.0\times {10}^3{\mathrm{Nm}}^{-1}$. What is the stretched length of the spring? If the body is pulled down further stretching the spring to a length of $5.9 \mathrm{cm}$ and then released, what is the frequency of oscillation of the suspended mass? (Neglect the mass of the spring).

Figure (a) shows a spring of force constant k fixed at one end and carrying a mass m at the other end placed on a horizontal frictionless surface. The spring is stretched by a force F.

Figure (b) shows the same spring with both ends free and a mass m fixed at each free end. Each of the spring is stretched by the same force F. The masses in both the cases, a and b are released. Find the maximum extension of the spring in both cases.

Figure (a) shows a spring of force constant k fixed at one end and carrying a mass m at the other end placed on a horizontal frictionless surface. The spring is stretched by a force F.

Figure (b) shows the same spring with both ends free and a mass m fixed at each free end. Each of the spring is stretched by the same force F. The masses in both the cases, a and b are released. Find the maximum extension of the spring in both cases.