A particular spring has a spring constant of 8. Suppose a 2 kg mass is hung on t

Question

A particular spring has a spring constant of 8. Suppose a 2 kg mass is hung on the spring and is
initially sent in motion with an upward velocity of 2 meters per second, 1/2 meter below the
equilibrium position.

A) Write down the DE that models the motion of this spring.
B) Write down the initial conditions.
C) Find the equation of motion for the spring.
D) Write the equation of motion in the form x(t) = Asin(wt +phi) or x(t) = Acos(wt +phi)
E) How many cycles would the spring %u2013 mass system complete in 20%u03C0 seconds?

Explanation / Answer

a) x"+(4)x = 0

b) t=.5 v=2m/s

c)eqn of spring = Ae^(2it)+Be^(-2ix)

it can be represented as Asin(wt+phi)

d) 2=2*sqrt(A^2-.5^2)

A=1.11 m

phi = -26.77 degree

last part is not clear

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