A block of mass m is attached to two unstrecthed of spring constant `k_1` and `k_2` as shown in the figure The block is displaced towards right through a distance x and is released. Find the speed of the block as it passes through the mean position shown.

A 1 kg block situated on a rough incline is connected to a spring of spring constant 100N m^-1 as shown in Fig. 6.17. The block is released from rest with the spring in the unstretched position. The block moves 10 cm down the incline before coming to rest. Find the coefficient of friction between the block and the incline. Assume that the spring has a negligible mass and the pulley is frictionless.

A block of mass M is places in the top of a biggr block of mass 10 M as shown in fig.All the surfaces are frictionless.The system is released from rest.Find the distance moved by the bigger block at the instant the smaller block reaches the ground. .

Two springs are joined and connected to a mass m . If the spring force constants are k_1 and k_2 show that the frequency of oscillation of mass m is

Consider a two - particle system with the particles having masses M_1 and M_2 .If the first particle is pushed towards the centre of mass through a distance a,by what distance whould the second particle be moved,so as t keep the centre of mass at the same position?

A metal bar AB can slide on two parallel thick metallic rails separated by a distance l. A resistance R and an inductance L are connected to the rails as shown in the figure. A long straight wire carrying a constant current I_(0) is placed in the plane of the rails and perpendicular to them as shown. The bar AB is held at rest at a distance x_(0) from the long wire. At t=0, it is made to slide on the rails away from wire. Answer the following questions. Find a relation among i, (di)/(dt) and (d phi)/(dt) , where i is the current in the circuit and phi is the flux of the megnetic field due to the long wire through the circuit.

A uniform electric field of strength 2xx10^3NC^-1 is established between two parallel plates of length 0.1 m held horizontally at a distance 0.02 m apart. An electron is projected at a speed of 6xx10^6 ms^-1 making an angle 45^@ as shown in the figure The field is directed vertically upwards. Will the electron strike the either plate? If it strikes the plate, where does it do so?

A mass of 2 kg is attached to the spring of spring constant 50 N m^-1 . The lock is pulled to a distance of 5 cm from its equilibrium position at x = 0 on a horizontal frictionless surface from rest at t = 0. Write the expression for tis displacement at anytime t.

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.

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.