1. Analog Computing. Consider an object thrown straight upward with an initial vertical velocity vo from an initial height h(0) 0

We will use the circuit below to do an analog calculation of thc altitude as a function of time.
vout (t) = klh(t)
Vo is fixed at Vo = kovo, where vo is the initial upward velocity. All Rs are equal and all Cs are equal. Assume all capacitors are initially discharged.
(a)   Write an expression for the output Vout(t), in terms of ko,Vo, R,C, and Vg.
(b)   Based on this, write expressions for kl and vg, such that Vout = klh(t), in terms of ko R, C, and g, where g is the (positive) deceleration of gravity, as shown. Be careful with signs!
(c)   Sketch a modified circuit witli O’ne component replaced (i.e. swap an R with a C or a C with an R), such that Vcut = klV(t), where v(t) is the vertical velocity as a function of time, rather than height. Write and expression for kl in terms of ko, R, and C. Again, bc careful with signs.