2. (a) 40.5-kg mass attaches to a spring and stretches it 0.98 cm. The spring/mass is then moved through a medium that imparts a damping force that's equal to the instantaneous velocity (so, beta = 1) Find the equation of motion if the spring/mass is released from rest at a point that is 75 cm below equilibrium. (b) ( Graph the equation of motion (you may attach a screenshot from a graphing calculator or Desmos, if you like). (c) The system above is modified so that there is an external driving force on the spring, given by the input function f(x)= e. Solve for the new equation of motion.
2. (a) 40.5-kg mass attaches to a spring and stretches it 0.98 cm. The spring/mass is then moved through a medium that imparts a damping force that's equal to the instantaneous velocity (so, beta = 1) Find the equation of motion if the spring/mass is released from rest at a point that is 75 cm below equilibrium. (b) ( Graph the equation of motion (you may attach a screenshot from a graphing calculator or Desmos, if you like). (c) The system above is modified so that there is an external driving force on the spring, given by the input function f(x)= e. Solve for the new equation of motion.
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Transcribed Image Text:2. (a)
40.5-kg mass attaches to a spring and stretches it 0.98 cm. The spring/mass is then moved
through a medium that imparts a damping force that's equal to the instantaneous velocity (so, beta = 1)
Find the equation of motion if the spring/mass is released from rest at a point that is 75 cm below
equilibrium.
(b) (
Graph the equation of motion (you may attach a screenshot from a graphing calculator or
Desmos, if you like).
(c)
Y
The system above is modified so that there is an external driving force on the spring, given
by the input function f(x)= e²t. Solve for the new equation of motion.
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