Simple Op Amp design for free fall

[CalcYouLater]

Homework Statement

Design a simple Op Amp circuit to find the position as a function of time of a falling body

Homework Equations

y=y_0+1/2gt^2

Assume y_0 = 0 at t=0

The Attempt at a Solution

I used an integrator Op Amp with a triangle wave input. I chose the values of the resistor and capacitor so that their product = 2.

This answer only seems to work part of the time. How can I design a simple circuit that is valid for all times?

 

[berkeman]

Homework Statement

Design a simple Op Amp circuit to find the position as a function of time of a falling body

Homework Equations

y=y_0+1/2gt^2

Assume y_0 = 0 at t=0

The Attempt at a Solution

I used an integrator Op Amp with a triangle wave input. I chose the values of the resistor and capacitor so that their product = 2.

This answer only seems to work part of the time. How can I design a simple circuit that is valid for all times?

To get the t^2 term, you need a non-linear element in the opamp circuit (diode or transistor junction). You can look up "opamp multiplier" or "opamp log converter" to get you farther. You will also need a reset button...