User talk:Egm4507.s13.team07.plicque

Solution
Kinematics:
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$$  \displaystyle y_c = y_k = y $$ (Eq.1.1)
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Kinetics:
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$$  \displaystyle my'' + f_I = f(t) $$     (Eq.1.2)
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$$  \displaystyle f_I = f_k +f_c $$     (Eq.1.3)
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Equations:
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$$  \displaystyle f_k = ky_k = ky $$ (Eq.1.4)
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$$  \displaystyle f_c = cy'_c = cy' $$     (Eq.1.5)
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By substitution of Eq. 1.4 and Eq. 1.5 into Eq. 1.3:
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$$  \displaystyle f_I = ky + cy' $$     (Eq.1.6)
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Then substituting Eq. 1.6 into Eq. 1.2:
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$$  \displaystyle my'' + cy' + ky =f(t) $$     (Eq.1.7) Which is the equation of motion of a spring-dashpot system in parallel with a mass m \, and applied force f(t).
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