Virtual Spring Feb. 23

Abstraction

We started off a new lesson with another abstraction. After the input voltage (RT/k, R=resistor T=torque and k=constant) enters the mystery box- the circuit - the output voltage results in -ΩKw. The actual circuit looks like the following diagram below.

In this diagram you can see the make up of the circuit. The virtual ground allows us to control the current on the motor.

To introduce virtual springs to the class, the equation for torque (T=-bw=iw,  i=current and w=speed) was compared to Newton's law F=ma (m=current and a=speed). Applying a torque proportional to the angular speed will create friction or damping so the object will ultimately slow down. For circuits when a motor is connected to a resistor the power is absorbed which slows it down. Similarly applying a torque proportional to the angular position will create a spring. Just like a pendulum, the energy in the spring switches from kinetic to potential energy.

To further explain the concept, the rate of change of position is angular speed and the rate of change of speed is acceleration. Here is the mathematical calculation to go from speed (w) to position. 

Note that a capacitor adds voltage to the circuit this is why you must add the input voltage (V+) to the voltage added by the capacitor (Vc) to obtain Vout. This is a rule of capacitors.

The abstraction for the calculation would show the input voltage (V+) going into the mystery box- circuit - and coming out as in output voltage (Vout in the calculation). When you put both abstractions together you end up creating a virtual spring.

 

Virtual Spring

We added two capacitors and a second potentiometer to our original motor circuit to create a virtual spring.

Circuit for virtual spring.

We were able to observe the spring in the circuit through the oscillator. When we held on to the motor the graph showed no change in the position and speed.

The position is represented by the blue line and the speed is represented by the yellow line.