A spring has force constant `k = 200 N//m` and its one end is fixed. There is a block of mass 2 kg attached to its other end and the system lies on a smooth horizontal table. The block is pulled so that the extension in the spring becomes 0.05 m. At this position the block is projected with a speed of `1 m//s` in the direction of increasing extension of the spring. Consider time t = 0 at the moment the block is projected and find
(a) the extension (or compression) in the spring as a function of time.
(b) the maximum extension in the spring and the time at which it occurs for the first time.
(c) the time after which the speed of the block becomes maximum for the first time. Given: `sin^(-1) (0.446) = 0.46` radian

Answer

`(a) x=0.112 sin (10t +046) m`
(b) 0.112 m, 0.111 s
(c ) t=0.268 s