An object weighing 8 pounds stretches a spring 2 feet. The object is initially r

Question

An object weighing 8 pounds stretches a spring 2 feet. The object is initially released from rest at a point 1 foot below the equilibrium position, and the subsequent motion takes place in a medium that offers a damping force that is equal to 2 times the instantaneous velocity. The object is driven by an external force equal to f(t) = 10 cos 4t. Answer the following for this scenario.

e. Find yc

f. Find yp using the method of undetermined coefficients.

g. Write the general solution y = yc + yp

h. Find the unknown constants using the initial conditions

i. Write the final equation of motion.

j. State any transient solutions

k. State any steady-state solutions

l. Using the graph paper make a well-labeled graph of the equation of motion and the steady-state solution. Explain why they look so much alike as t gets large.

Explanation / Answer

An object weighing 8 pounds stretches a spring 2 feet. The object is initially r

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