Spring/Mass systems:
Free undamped equation:
Suppose that a flexible spring is suspended vertically from a rigid support. An object
of mass m = 0.2 kg is attached to its free end and stretches the spring Δx = 5 / 8 m.
(1) At t = 0 , the object is released from a point 2/3m below the equilibrium position
with an upward velocity of 4/3 m/s. Find the position of the object as a function of
time x(t) . (Let us assume the free-fall acceleration g = 10.0 m / s2 .)
Undamped forced motion:
(2) Suppose we now take into consideration an external force f(t) = f0 sinγt acting
on the same spring with γ = 2 rad/s and f0 = 1N, and the initial conditions:
x(0) = 0 , x´(0) = 0 . Find the position of the oscillating object as a function of
time x(t) .
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