The equation for the line of best fit was determined to be y=0.038sin(9.56t+0.20)−0.09, where t is time in seconds and y is displacement in meters. The team used a 1 kilogram mass which displaced the spring 0.09 meters below equilibrium. We can use their initial conditions of y(0)=−0.083 and the fact that the spring was released from rest – thus y′(0)=0. Your job is to build the equation of motion for this spring. The damping coefficient c is unknown, but can you make a decent estimate for the value of c? Please consider whether the spring should be under/over/critically damped based on what you understand of the context. This can help you determine a value, or at least a range of possible values, for c. Compare and contrast the two displacement models. What caused the differences? Which one do you think is better?
The equation for the line of best fit was determined to be y=0.038sin(9.56t+0.20)−0.09, where t is time in seconds and y is displacement in meters. The team used a 1 kilogram mass which displaced the spring 0.09 meters below equilibrium. We can use their initial conditions of y(0)=−0.083 and the fact that the spring was released from rest – thus y′(0)=0. Your job is to build the equation of motion for this spring. The damping coefficient c is unknown, but can you make a decent estimate for the value of c? Please consider whether the spring should be under/over/critically damped based on what you understand of the context. This can help you determine a value, or at least a range of possible values, for c. Compare and contrast the two displacement models. What caused the differences? Which one do you think is better?
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