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=6.3 kg is attached to the end of a spring with a spring constant of k=18.1 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=0.362J

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= ?????
(for second question, please give me a specific answer..I know that I need run vpython to solve it, however there is no vpython in my computer .)

Explanation / Answer

We can ust the spring potential formula to solve the first one

Ei = (1/2) * k * x2

so Ei = (1/2) * 18.9 * .22 = 0.378 J

# Constants pi = 3.14159 L0 = .08

# equilibrium length of spring (not stretched) g = 0

# gravitational acceleration set to zero (not on earth) k = 14

# insert the spring constant you found for the coiled spring

# Objects

# Ceiling to hang spring from.

# block to act as mass.

# Spring is represented by a cylinder. scene.center = vector(0,-.1,0)

# you may want to adjust this to improve display ceiling = box(pos=vector(0,0,0), size=(.3,0.005,0.005))

# make the contact pointthe origin block=box(pos=vector(0,-0.1,0), size=(.02,0.02,0.02), color=color.yellow)

# Using the positions of the block and ceiling set the cylinder to stretch from the ceiling to the block spring = cylinder(pos=ceiling.pos, axis=block.pos, radius=.005)

# Initial values block.m = 0.45

# insert the measured mass from coiled spring experiment. block.v = vector(0,0,0)

# the vector velocity assuming the block is initially stationary block.p= block.m * block.v block.pos=vector(0,-L0-0.05,0)

# initial position of block 0.05m from equilibrium

# Setting the timestep and zeroing the cumulative time deltat = .0001

# you should decrease this later to test if it is small enough t = 0 W = 0 displacement=0 Kgraph = gcurve(color=color.cyan) Ugraph = gcurve(color=color.yellow) KplusUgraph = gcurve(color=color.red) Wgraph = gcurve(color=color.green)

# Loop for repetitive calculations scene.autoscale=0 while t < 4: Fnet= -(((block.pos-vector(0,-L0,0))*k))-((block.p/block.m)*.2)

#INSERT the force of the spring on the block displacement=(mag(block.p)/block.m)*deltat block.p= block.p+Fnet*deltat

# updates the momentum block.pos= block.pos+block.p/block.m*deltat

# updates the position spring.axis = block.pos #updates the spring axis so it stays on the block t=t+deltat pmag = mag(block.p)

# or whatever you've called the block's momentum K = (pmag**2)*.5/block.m

#COMPLETE this for the kinetic energy of the block U = ((mag(block.pos)-L0)**2)*.5*k

#COMPLETE this for the potential energy of the block-spring system (note no gravity) W = W - displacement*(mag(block.p)/block.m)*.2 Kgraph.plot(pos=(t,K)) Ugraph.plot(pos=(t,U)) KplusUgraph.plot(pos=(t,K+U)) Wgraph.plot(pos=(t,W))

For solving the second part we need top look at the graph in VPython of the total energy, kinetic energy, and potential energy.We can get to know that 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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