An elastic spring has a mass suspended at its lower end, its upper end being fixed to support. The mass is puled down to a certain distance and released. Calculate the time period of its oscilaltions.

A spring having with a spring constant 1200 N m^-1 is mounted on a horizontal table as shown in Fig. 14.24. A mass of 3 kg is attached to the free end of the spring. The mass is then pulled sideways to a distance of 2.0 cm and released.Determine the frequency of oscillations,

A spring having with a spring constant 1200 N m^-1 is mounted on a horizontal table as shown in Fig. 14.24. A mass of 3 kg is attached to the free end of the spring. The mass is then pulled sideways to a distance of 2.0 cm and released.Determine the maximum speed of the mass

A spring having with a spring constant 1200 N m^-1 is mounted on a horizontal table as shown in Fig. 14.24. A mass of 3 kg is attached to the free end of the spring. The mass is then pulled sideways to a distance of 2.0 cm and released.Determine maximum acceleration of the mass,

A circular disc of mass 10 kg is suspended by a wire attached to its centre. The wire is twisted by rotating the disc and released. The period of torsional oscillations is found to be 1.5 s. The radius of the disc is 15 cm. Determine the torsional spring constant of the wire. (Torsional spring constant alpha is defined by the relation J = -alphatheta , where J is the restoring couple and 0 the angle of twist).

A body of mass m is attached to one end of a massless spring which is suspended vertically from a fixed point. The mass is held in hand so that the spring is neither stretched nor compressed. Suddenly the support of the hand is removed. The lowest position attained by the mass during oscillation is 4 cm below the point, where it held in hand. What is the amplitude of oscillation?

A body of mass m is attached to one end of a massless spring which is suspended vertically from a fixed point. The mass is held in hand so that the spring is neither stretched nor compressed. Suddenly the support of the hand is removed. The lowest position attained by the mass during oscillation is 4 cm below the point, where it held in hand. Find the frequency of oscillation?

An air chamber of volume V has a neck area of cross section a into which a ball of mass mjust fits and can move up and down without any friction (Fig.14.27). Show that when the ball is pressed down a little and released , it executes SHM. Obtain an expression for the time period of oscillations assuming pressure-volume variations of air to be isothermal [see Fig. 14.27

Figure 14.26 (a) shows a spring of force constant k clamped rigidly at one end and a mass m attached to its free end. A force F applied at the free end stretches the spring. Figure 14.26 (b) shows the same spring with both endsfree and attached to a mass m at either end. Each end of the spring in Fig. 14.26(b) is stretched by the same force F If the mass in Fig. (a) and the two masses in Fig. (b) are released, what is the period of oscillation in each case ?