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Unformatted text preview: ic Motion: Suppose an object of
mass m is suspended from a spring with spring constant k . If the initial displacement from the
equilibrium position is x0 and the initial velocity of the object is v0 , then the displacement x from
the equilibrium position at time t is given by x(t) = A sin(ωt + φ) where
• ω= k
and A =
m x2 +
ω 2 • A sin(φ) = x0 and Aω cos(φ) = v0 .
It is a great exercise in ‘dimensional analysis’ to verify that the formulas given in Theorem 11.1
work out so that ω has units 1 and A has units ft. or m, depending on which system we choose.
Example 11.1.3. Suppose an object weighing 64 pounds stretches a spring 8 feet.
1. If the object is attached to the spring and released 3 feet below the equilibrium position from
rest, ﬁnd the equation of motion of the object, x(t). When does the object ﬁrst pass through
the equilibrium position? Is the object heading upwards or downwards at this instant?
2. If the object is attached to the spring and released 3 feet bel...
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