weight of passengers = 360 * 9.81 = 3532 Newtons
distance they compressed spring = x = 0.04 meters
F = kx
3532 = k (0.04)
k = 88,290 Newtons/meter
then assume x = A sin (2 pi t/T)
then
v = A(2 pi/T) cos (2 pi t/T)
a = -A (2 pi / T)^2 sin (2 pi t/T) = - (2 pi /T)^2 x
then
-F = m a (- F because force by spring on mass, not by weight on spring)
- k x = - 900(2 pi /T)^2
-88,290 = - 900(2 pi/T)^2
2 pi/T =9.90
T = 0.634 second
in a certain automobile when five passenger get in their total mass being 360kg the spring of the suspension are compressed a distance 4cm. the total mass including the passenger supported by the suspension is 900kg. assuming that the displacement of the spring is directly proportional to the compressive force in them calculate the period of oscillation
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