There is a 1kg bucket suspended by a single linear flexible

There is a 1kg bucket suspended by a single linear flexible stretch sensor. The stretch sensor behaves like a system with parallel spring and damper. The spring constant k=2 and damping b=8. A 1kg brick is dropped into the bucket. The bucket, before the brick is dropped in, is at its equilibrium point. At this equilibrium point the stretch sensor is measured to have a resistance of 3000 ohms. The resistance increases by 50 ohms for every centimeter it is stretched. It is assumed that the stretch sensors will not break. Design a Schmitt trigger circuit to make a single determination that the brick has been dropped in the bucket. A 5V output is desired to represent that a brick has been dropped into the bucket and 0V otherwise. Your power supply is a 12V battery; you have an LM311 comparator, any standard resistor value, any standard capacitor value, aLMC7805 voltage regulator, and wire. What is the model used to describe this system? What is the position as a function of time? What is the resistance of the stretch sensor as a function of time? How will you use the sensor to provide an input for the Schmitt trigger? What voltage thresholds will you use to design the circuit? What are the design equations for a Schmitt trigger circuit? Choose thresholds for the Schmitt trigger levels. Why choose what you did? Draw the final circuit diagram for this design, including the power supply. Show all workings, design assumptions made, and rationale for decisions.

Solution

a) system model consist of output feedback given to input as o/p depends in i/p

b) Y(s) = 9.8 /(s² + 8s +s)

   = e^-9.8t sin 6.4t

c) resistance of the sensor = 3000/2 = 1500 ohm\'

d) Vth = 1.5