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.

Explanation

The effective force constant of the spring system is `2k` (since they constitute a parallel combination). The angular frequency of simple harmonic oscillation is
`omega sqrt(2k)/(m) sqrt(2xx0.5)/(0.010) 10 rad//s`
the amplitude` A=0.02 m`
The speed of the paper may be assumed as the speed of wave`-`propagators and the curve traced on the paper can be represented by the equation

`y omega A sin(omegat-kx)`..`(i)`
The wavelength
`lambda=(v)/(f)=(v)/(omega//2pi)=(2pi)/(omega)=(2pixx0.1)/(10)=(pi)/(50)m`..`(ii)`
`:.` `k=(2pi)/(lambda)=(omega)/(v)=(10)/(0.1)=100`
substituting the value in `(i)`, we get the required equation of the path
`y=A sinkx=0.02 sin (100x)`