A particle of mass m is attached to one end of a mass-less spring of force constant k, lying on a frictionless horizontal plane. The other end of the spring is fixed. The particle starts moving horizontally from its equilibrium position at time `t=0` with an initial velocity `u_0`. when the speed of the particle is `0.5u_0`, it collides elastically with a rigid wall. After this collision

A small block of mass m is attached to free end of a spring of force cosntant k , whose other end is fixed to a rigid support . The block is lying on a frictionless horizontal plane and it starts movi0ng away from fixed end of the spring a\t t= 0 with intial velocity u When the speed of the block is 0.6mu it collides with a fixed heavy mass elastically. After the collision with a fixed heavy mass elastically . Aftere the collision the time at which the block passes through its equilibrium position for the first time is close to

A 10 kg mass is connected at one end of a massless spring with force constant k = 1000 N/m, keeping other end fixed in a horizontal plane as shown in the fig. 15.6 If the sytem is displaced by 0.01 m from its equilibrium position A to a point B, then the acceleration of the system is

A ring of mass m is attached to a horizontal spring of spring constant k and natural length l_0 . The other end of the spring is fixed and the ring can slide on a horizontal rod as shown. Now the ring is shifted to position B and released Find the speed of the ring when the spring attains its natural length.

A particle of mass 'm' attached with one end of a light spring of stiffness (k) is pushed with a speed (v) on a smooth horizontal plane. If l_(0)= natural length of the spring and x_(0) = elongation of the spring at the given instant.

A particle of mass m is attached to one end of a light inextensible string and the other end of the string is fixed in vertical plane as shown. Particle is given a horizontal velocity u = sqrt((5)/(2)gl) The tension in the string at an instant when acceleration of the particle is horizontal and sqrt(3)g is

A block of mass m is attached to one end of a mass less spring of spring constant k. the other end of spring is fixed to a wall the block can move on a horizontal rough surface. The coefficient of friction between the block and the surface is mu then the compession of the spring for which maximum extension of the spring becomes half of maximum compression is .

A block of mass m is attached to one end of a mass less spring of spring constant k. the other end of spring is fixed to a wall the block can move on a horizontal rough surface. The coefficient of friction between the block and the surface is mu then the compession of the spring for which maximum extension of the spring becomes half of maximum compression is .

A block of mass m, lying on a smooth horizontal surface, is attached to a spring (of negligible mass) of spring constant k. The other end of the spring is fixed, as shown in the figure. The block is initally at rest in its equilibrium position. If now the block is pulled withe a constant force F, the maximum speed of the block is :