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.

a. What is the mass of the object?

b. What is the constant for the spring?

c. Write the differential equation for the scenario.

d. What are the initial conditions?

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

As per multiple qustions/subparts rules, we are supposed to answer the the first subparts of the first question.

We have answered the first four subparts of the question.

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