Use your program for the viscously damped spring to solve this problem. Make sur

Question

Use your program for the viscously damped spring to solve this problem. Make sure you change the parameters as specified below. A mass m=8.8 kg is attached to the end of a spring with a spring constant of k=18.6 N/m. The mass moves through a viscous damping medium with a damping constant b=1.8 kg/s giving a velocity dependent damping force Fdamp= -bv. The motion occurs in zero gravity so set the force of gravity to ZERO in your program. Also set the equilibrium position L0=0. The mass is initially motionless and displaced from equilibrium by a distance yinitial=0.2 m. What is the energy of the spring-mass system at the initial position of the mass? (the spring-mass system does not include the damping medium) Einitial= Correct: Your answer is correct. J What is the energy of the spring-mass system when the mass first passes through the equilibrium position? (you may wish to include a logical test to help you find when this occurs) Efinal=

Explanation / Answer

Given
mass m = 8.8 kg
spring constant k = 18.6 N/m
damping constant b = 1.8 kg/s
y initial = 0.2 m

In order to answer the first question, you have to use the spring potential formula

its Ei = (1/2) * k * x^2
so Ei = (1/2) * 18.6 * 0.2^2 = 0.372 J

However, the second part requires you to look at you graph in VPython of the total energy, kinetic energy, and potential energy. The energy of the spring-mass system when the mass first passes through the equilibrium position lies where your total energy meets the first peak of kinetic energy

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