One end of each of two identical springs, each of force constant `0.5N//m` are attached on the opposite sides the a wooden block of mass `0.01kg`. The other ends of the spring are connected to separate rigid supports such that the springs are unstrtched and are collinear in a horizontal plane. To the wooden piece is fixed a pointer which touches a vertically moving plane paper. The wooden piece kept on a smooth horizontal table is now displaced by `0.02m` along the line of springs and released. If the speed of paper is `0.1m//s`, find the equation of the path traced by the pointer on the paper and the distance between two consecutive maximum on this path.

Answer

A, B, C

Explanation

`k_(eff) = 2k = 1.0 N//m`
`f = (1)/(2pi) sqrt(k_(eff)/(m)) = (10)/(2pi)s^(-1)`
`v=0.1 m/s , A =0.02 m`
`lambda=(v)/(f) = (0.1)/(((10)/(2pi))) = (2pi)/(100)m`
`y = A cos ((2pi)/(lambda)) (vt - x)`
`=0.02 cos 100(0.1t - x)`
`=0.02 cos (10t - 100x)m`
The distance between two successive maxima
`= lambda = (2pi)/(100) =0.0628 m`