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=5 kg is attached to the end of a spring with a spring constant of k=18.2 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 when the mass first passes through the equilibrium position? (you may wish to include a logical test to help you find when this occurs)

I do not have VPython, but my understanding is that  the energy of the spring-mass system when the mass first passes through the equilibrium position lies where the total energy meets the first peak of kinetic energy.

Explanation / Answer

Energy is given as E = 1/2(K*A^2*e^-(b/2m)t)

when mass first passes through its equilibrium position time = T(time period)/4

time period T = 2*pi*sqrt(m/k) =3.29s

so t = T/4

t = 0.82s

By putting all values and solving we get

E = 0.32J

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