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?

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 0.5 kg mass is suspended vertically from a point fixed on the Earth by a spring having a stiffness of 5 N/mm. What is its static displacement in (mm and m)? Solve by changing the unit into 'm' as well as 'mm'.

A small stone of mass 200 g is tied to one end of a string of length 80 cm . Holding the other end in hand , the stone is whirled into a vertical circle What is the minimum speed that needs to be imparted at the lowest point of the circular path , so that the stone is just able to complete the vertical circle ? what would be the tension at the lowest point of circular path ? (Take g = 10 m//s^(2) ) .

A point particle of mass M is attached to one end of a massless rigid non-conducting rod of length L. Another point particle of the same mass is attached to the other end of the rod. The two particles carry charges +q and -q respectively. This arrangement is held in a region of a uniform electric field E such that the rod makes a small angle theta (say of about 5 degree) with the field direction, fig. Find an expression for the minimum time needed for the rod to become parrallel to the field after it is set free.

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 ?

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,

Two bodies of masses 1 kg and 3 kg respectively are connected rigidly by a vertical spring. The body of mass 3 kg rests on a smooth horizontal surface. The force constant of the spring is 484Nm^(-1) . From the equilibrium position, the mass of 1 kg is displaced vertically through a distance of 0.02 m and then released. calculate (i) and frequency of oscillation of the mass of 1 kg (ii) the maximum velocity of this mass (iii) its oscillation energy and (iv) the reaction of the table on the mass of 3 kg, when mass 1 kg is having harmonic oscillations.

A magnet is suspended vertically from a fixed point by means of a spring, as shown in the figure. One end of the magnet hangs inside a coil of wire. The coil is connected in series with a resistance R. The magnet is displaced vertically a small distance D and the released. shown in the figure variation with time t of the vertical displacement d of the magnet from its equilibrium position. State and explain, by reference to electromagnetic induction, the nature of the oscillations of the magnet. Calculate the angular frequency omega_0 of the oscillations.

The masses m_1 and m_2 together are suspended from a massless spring of constant k. When masses are in equilibrium, m_2 is removed without disturbing the system. Find the amplitude of oscillation and angular frequency of m_1

A stone of mass and spring constant k. The unstrecthed length of the string is L and has negligible mass. The other end of the string is fixed to a nail at a point P. Initially the stone is at the same level as the point P. The stone is dropped vertically from point P. Find the distance y from the top when the mass comes to rest for an instant, for the first time.