A plank with a body of mass `m` placed on it starts moving straight up according to the law `y = a(1 - cos omega t)`, where `y` is the displacement from the initial position, `omega = 11 rad//s`. Find
(a) The time independence of the force that the body exerts on the plank.
(b) The minimum amplitude of oscillations of the plank at which the body starts falling behind the plank.

Answer

A, B, C

Explanation

(a) `y = a(1 - cos omega t)`
`(d^(2)y)/(dt^(2)) = a omega^(2)cos omega t`
`N - mg = m.(d^(2)y)/(dt^(2))`
or `N = mg + m a omega^(2) cos omega t`
or `N = m(g + a omega^(2) cos omega t)`
(b) `((d^(2)y)/(dt^(2)))_(max) = a omega ^(2)` or `aomega^(2) = g`
`:. a = (g)/(omega^(2)) = (980)/((11)^(2))`
` = 8.1 cm` .