A block of mass 2 kg is attached to one end of a massless spring whose other end is fixed at a wall. The spring-mass system moves on a frictionless horizontal table. The spring's natural length is 2 m and spring constant is 200 ~N / m . The block is pushed such that the length of the spring becomes 1 m and then released. At distance x m ( x 2) from the wall. the speed of the block will be :

Step-by-step solution

Given, Natural length of spring =2 ~m Initial compression in spring ( x _ i )=1 ~m Final compression in spring ( x _ f )=(2- x ) m Using energy conservation aligned & K _ i + U _ i = K _ f + U _ f & 0+ 1 2 Kx _ i ^2= 1 2 mv ^2+ 1 2 Kx _ f ^2 & 1 2 mv ^2= 1 2 ~K ( x _ i ^2- x _ f ^2 ) & 1 2 2 v ^2= 1 2 200 (1^2-(2- x )^2 ) & v ^2=100 [1-(2- x )^2 ] & v =10 [1-(2- x )^2 ]^ 1 / 2 aligned