Please answer all of these questions Please note This is Mathematica lab It have

Question

Please answer all of these questions

Please note

This is Mathematica lab
It have to be done by Mathematica software.

Lab #3 Exercises 1. Find the equation of motion and graph of the systern that has an associated DE: 2. Redo exercise 1 when the weight is released 1/2 ft above equilibrium with downward initial velocity of 5ft/sec. 3. A 128 lb weight stretches a spring 6.4 ft. The medium through which the weight moves offers a resistance numerically equal to 2 times the instantaneous velocity. The weight is released 2 feet above equilibrium with a downward velocity of 5 ft/sec. a. Set up the system b. Find the equation of motion c Graph it. d. What is the maximum displacement of the mass on the spring? e. What is the velocity of the mass in 1 second, 5 seconds? 4. Using the system in exercise 3, find the equation of motion and graph when there is an external force, fit)- SCosl4tl, acting on the system. Discuss the change in the graph and how the external force affected the system.

Explanation / Answer

Answer:

1)

Solution of Equation of Motion is

x(t) = e^-4t * t
so Y = (e^-4 x) * x

now,
x(0) = -1/2 ft
velocity of equation = x'(0) = 5 ft/sec

consider downword direction as +ve.

we have solution as :

x(t) = 0.5 * e^(-4t) * (6t-1)
so that
Y = 0.5 * (e^(-4x))* (6x-1)

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