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In our present setting, the force involved is weight which is caused by the acceleration due to gravity.
Note that 1 pound = 1 slug foot and 1 Newton = 1 kg meter .
Look familiar? We saw Hooke’s Law in Section 4.3.1.
To keep units compatible, if we are using the English system, we use feet (ft.) to measure displacement. If we
are in the SI system, we measure displacement in meters (m). Time is always measured in seconds (s).
9 11.1 Applications of Sinusoids 753 in our case is air). The following theorem, which comes from Diﬀerential Equations, gives x(t) as
a function of the mass m of the object, the spring constant k , the initial displacement x0 of the
object and initial velocity v0 of the object. As with x(t), x0 = 0 means the object is released from
the equilibrium position, x0 < 0 means the object is released above the equilibrium position and
x0 > 0 means the object is released below the equilibrium position. As far as the initial velocity v0
is concerned, v0 = 0 means the object is released ‘from rest,’ v0 < 0 means the object is heading
upwards and v0 > 0 means the object is heading downwards.13
Theorem 11.1. Equation for Free Undamped Harmon...
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