A massless spring of spring constant K = 100 N/m hangs in a vertical plane from point O. Its other end is attached with a block of mass m = 2kgand system is in equilibrium .Now another small spherical ball of same mass moving with a velocity `v_0`=`sqrt10`m/s collides with the block and get stuck to it .The new amplitude of oscillation will be.

Two block A and B of masses m_(1) = 3kg and m_(2) = 6kg respectively are connected with each other by a spring of force constant k = 200 N//m as shown in figure. Blocks are pulled away from each other by x_(0) = 3cm and then released. When spring is in its natural length and block are moving towards each other, another block C of mass m = 3kg moving with velocity v_(0) = 0.4m//s (towards right) collides with A and gets stuck to it. Neglecting friction, calculate (a) velocity v_(1) and v_(2) of the blocks A and B respectively just before collision and their angular frequency . (b) velocity of centre of mass of the system, after collision, ( c) amplitude of oscillation of combined body, (d) loss of energy during collision.

A spring block pendulum is shown in figure . The system is hanging in equilibrium. A bullet of mass m//2 moving at a speed u bites the block from downwards direction and gets embedded in it. Find the amplitude of oscillation of the block now.

Consider a block of mass 'm' attached to a spring of spring constant 'K' as shown. Now a block of same mass 'm' moving with velocity 'u' strikes the other block and stick to it. Both blocks collectively start performing SHM . The amplitude (A) of their SHM is

One end of an ideal spring is fixed to a wall at origin O and axis of spring is parallel to x-axis. A block of mass m = 1kg is attached to free end of the spring and it is performing SHM. Equation of position of the block in co-ordinate system shown in figure is x = 10 + 3 sin (10t) . Here, t is in second and x in cm . Another block of mass M = 3kg , moving towards the origin with velocity 30 cm//s collides with the block performing SHM at t = 0 and gets stuck to it. Calculate (a) new amplitude of oscillations, (b) neweqution for position of the combined body, ( c) loss of energy during collision. Neglect friction.

One end of an ideal spring is fixed to a wall at origin O and axis of spring is parallel to x-axis. A block of mass m = 1kg is attached to free end of the spring and it is performing SHM. Equation of position of the block in co-ordinate system shown in figure is x = 10 + 3 sin (10t) . Here, t is in second and x in cm . Another block of mass M = 3kg , moving towards the origin with velocity 30 cm//s collides with the block performing SHM at t = 0 and gets stuck to it. Calculate (a) new amplitude of oscillations, (b) neweqution for position of the combined body, ( c) loss of energy during collision. Neglect friction.

A block of mass m suspended from a spring of spring constant k . Find the amplitude of S.H.M.

Consider a block of mass 'm' attached to a spring of spring constant 'K' as shown. Now a block of same mass 'm' moving with velocity 'u' strikes the other block and stick to it. Both blocks collectively start performing SHM . Choose the correct option(s) :

In Fig. a pulley is shown which is frictionless and a ring of mass m can slide on the string without any friction. One end of the string is attached to point B and to the other end, a block 'P' of mass m is attached. The whole system lies in vertical plane. Now another block 'C' of same mass m is attached to the block 'P' and system is released from rest. If a_(1) and a_(2) are the magnitudes of initial accelerations of ring and blocks, respectively, then

A block of mass 'm' is hanging from a massless spring of spring constant K . It is in equilibrium under the influence of gravitational force. Another particle of same mass 'm' moving upwards with velocity ao hits the block and sticks to it. For the subsequent motion, choose the incorrect statements:

In figure, a block A of mass 2kg is moving to the right with a speed 5m//s on a horizontal frictionless surface. Another block B of mass 3kg a massless spring of spring constant 222N//m attached to it, is moving to the left on the same surface and with a speed 2m//s . Let us take the direction to the right as the positive X- direction. At some instant, block A collides with the spring attached to block B . At some other instant , the spring has maximum compression and then, finally, blocks move with their final velocities. Assuming that (i) the spring force is conservative and so there is no conversion of kinetic energy to internal energy and (ii) , no sound is made when block A hits the spring, answer the following questions. When the blocks are yet to attain their final velocities, in this situation at any instant when block A is moving with a velocity 4 hat(i) m//s , velocity of block B will then be :