A person normally weighing 50kg stands on a massless platform which oscillates up and down harmonically at a frequency of `2.0 s^(-1)` and an amplitude `5.0 cm`. A weighing machine on the platform gives the persons weight against time.
If answer of part (1) is yes, what will be the maximum and minimum reading in the machine and at which position?

Explanation

Here, oscillations are periodic hence acceleration changes. The weight of man depend on direction of acceleration and its magnitude in up and down motion.
(b) The acceleration is maximum at two extreme points of the platform.
At upper extreme point acceleration on platform is in downward,
From equation of motion
`N= mg - ma`
`N= mg - m omega^(2) A`
`therefore N= m[g- omega^(2)A]`
`=50[9.8-4pi^(2)v^(2)A]`
`=50[9.8-4xx(3.14)^(2) xx 4 xx 5xx 10^(-2)]`
`=50[9.8-7.88]= 50[1.92]`
Weight = 96N and at mean position
`N= mg`
`=50xx 9.8`
Weight = 490 N
At lower extreme point,
`N= mg+ ma`
`= m(g+a)`
`=m(g + omega^(2)A)`
`=m(g+ 4pi^(2)v^(2)A)`
`=50(9.8+4xx(3.14)^(2)xx (2)^(2)xx5 xx 10^(-2))`
`=50(9.8+7.88)`
`=50(17.68)`
Weight = 884 N.