Suppose that a 7kg mass is attached to the end of a spring and hangs down vertic

Question

Suppose that a 7kg mass is attached to the end of a spring and hangs down vertically, streching the spring by 20mm. Then, the mass is pulled down another 10mm and released with no initial velocity. (a) Determine the spring constant k. (b) Giving numerical values for all constants, state the initial value problem for the displacement y(t) (measured in meters) of the mass from its equilibrium rest position. Assume that y(t) is measured positive in the downward direction. (c) Solve the initial value problem formulated in part (b).

Explanation / Answer

F= KX

K = F/X

= 7 g /20*10^-3 = 350g

b)my'' +k y = 0 (y'' is the acceleration in the downward direction, ky is the force in the upward direction)

y(0) = 10^-2 , y'(0) = 0

c) solution is

y(t) = 10^-2 cos(sqrt(k/m)) t

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