In questions 1, find the function that shows the time dependent change of the position of the given undamped spring-mass system. Determine the period and amplitude of the motion. Determine how many seconds after t = 0 the system first passes the maximum position (in the positive or negative direction) and the equilibrium position. (You will find the spring constant k yourself. Please make sure that the units you use are compatible with each other. For simplicity, you can use seconds as time units, kilograms as mass units, meters as displacement units. For gravitational acceleration, you can use g = 10 m/s². Get help from the calculator in your transactions.) 1. A massless spring, when a mass of 50 grams is attached to its end, moves 10 centimeters down from its equilibrium position and stays in balance in this position. This spring-mass system is pulled down 0.2 meters from this new equilibrium position and released at the first speed.

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In questions 1, find the function that shows the time dependent change of
the position of the given undamped spring-mass system. Determine the
period and amplitude of the motion. Determine how many seconds after t =
0 the system first passes the maximum position (in the positive or negative
direction) and the equilibrium position. (You will find the spring constant k
yourself. Please make sure that the units you use are compatible with each
other. For simplicity, you can use seconds as time units, kilograms as mass
units, meters as displacement units. For gravitational acceleration, you can
use g = 10 m/s². Get help from the calculator in your transactions.)
1. A massless spring, when a mass of 50 grams is attached to its end, moves
10 centimeters down from its equilibrium position and stays in balance in
this position. This spring-mass system is pulled down 0.2 meters from this
new equilibrium position and released at the first speed.
Go to https://www.geogebra.org/m/utcMvuUy website. After transforming the
problem you solved in question 1 into a differential equation system, enter the
system in the "x'(t)" and "y'(t)" boxes on the upper left side of the interactive
window in the site content, and then click somewhere on the window to draw the
phase diagram of the system. . While the phase diagram is being drawn, take the
printout of the page and indicate the direction in which time is flowing by drawing
an arrow with your pen. Then, mark the following moments on the diagram with a
pencil, denoted by the period T of the mass-spring system you solved in Question 1:
- moment t=0
- The first moment when the mass-spring system passes the maximum amplitude
after t=0
- The first moment when the mass-spring system passes the minimum amplitude
after t=0
- The first moment in which the mass-spring system passes the equilibrium position
after t=0
- t = T/2
-t=T
Transcribed Image Text:In questions 1, find the function that shows the time dependent change of the position of the given undamped spring-mass system. Determine the period and amplitude of the motion. Determine how many seconds after t = 0 the system first passes the maximum position (in the positive or negative direction) and the equilibrium position. (You will find the spring constant k yourself. Please make sure that the units you use are compatible with each other. For simplicity, you can use seconds as time units, kilograms as mass units, meters as displacement units. For gravitational acceleration, you can use g = 10 m/s². Get help from the calculator in your transactions.) 1. A massless spring, when a mass of 50 grams is attached to its end, moves 10 centimeters down from its equilibrium position and stays in balance in this position. This spring-mass system is pulled down 0.2 meters from this new equilibrium position and released at the first speed. Go to https://www.geogebra.org/m/utcMvuUy website. After transforming the problem you solved in question 1 into a differential equation system, enter the system in the "x'(t)" and "y'(t)" boxes on the upper left side of the interactive window in the site content, and then click somewhere on the window to draw the phase diagram of the system. . While the phase diagram is being drawn, take the printout of the page and indicate the direction in which time is flowing by drawing an arrow with your pen. Then, mark the following moments on the diagram with a pencil, denoted by the period T of the mass-spring system you solved in Question 1: - moment t=0 - The first moment when the mass-spring system passes the maximum amplitude after t=0 - The first moment when the mass-spring system passes the minimum amplitude after t=0 - The first moment in which the mass-spring system passes the equilibrium position after t=0 - t = T/2 -t=T
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