One end of each of two identical springs, each of force constant 0.5 N/m are attached on the opposite sides of a wooden block of mass 0.01 kg. The other ends of the springs are connected to separate rigid supports such that the springs are unstretched and collinear in horizontal plane. To the wooden piece is fixed a pointer which touches a vertically moving plane of paper. The wooden piece kept on a smooth horizontal table is now displaced by 0.02 m along the line of spring and released. If the speed of the paper perpendicular to the length of the springs is 0.1 m/s, the distance between two consecutive maxima on the path is $\frac{π}{n}$ then find n value?

Question

One end of each of two identical springs, each of force constant 0.5 N/m are attached on the opposite sides of a wooden block of mass 0.01 kg. The other ends of the springs are connected to separate rigid supports such that the springs are unstretched and collinear in horizontal plane. To the wooden piece is fixed a pointer which touches a vertically moving plane of paper. The wooden piece kept on a smooth horizontal table is now displaced by 0.02 m along the line of spring and released. If the speed of the paper perpendicular to the length of the springs is 0.1 m/s, the distance between two consecutive maxima on the path is $\frac{π}{n}$ then find n value?

Accepted Answer

keq=2kThe angular frequency of simple harmonic oscillation is given byω=2km=2×0.50.01=10  rad  s−1∴f=ω2π=5πHzA=0.02  mThe speed of paper may be assumed as the speed of wave propagation.∴λ=vf=0.15/π=π50m

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