Series RLC step response, step by step — a TI-89 Titanium program

By E-Code · updated 2026-09-26

RLCSTEP is a TI-89 BASIC program for the TI-89 Titanium. A series RLC circuit switched onto a DC voltage from rest. Step by step: the circuit equation, the characteristic equation and its roots from the CAS (complex when underdamped), the damping ratio and case, the general solution, the initial conditions solved for the constants, then peak time, overshoot and settling time.

What it asks for and what it shows

It asks for 4 values at its prompts. In the example below it shows α=R/(2L), ω0=1/√(LC), ζ=α/ω0, k2, k1, ωd=√(ω0²-α²), tp=π/ωd s, vC(tp) V, OS %, ts=4/α s, UNDERDAMPED (ζ<1), 2 CHARACTERISTIC EQ, 6 SOLVE BOTH (CAS), 8 ANSWER.

Example run

One of its oracle test cases. The inputs are typed in order, and the results are the values the case expects on the screen.

Step	Value
You enter
Input 1	10
Input 2	0.1
Input 3	0.001
Input 4	12
The screen shows
`α=R/(2L)=`	50
`ω0=1/√(LC)=`	100
`ζ=α/ω0=`	0.5
`k2=`	-6.92820323
`k1=`	-12
`ωd=√(ω0²-α²)=`	86.60254038
`tp=π/ωd s=`	0.03627598728
`vC(tp) V=`	13.95640242
`OS %=`	16.30335348
`ts=4/α s=`	0.08
Text	UNDERDAMPED (ζ<1)
Text	2 CHARACTERISTIC EQ
Text	6 SOLVE BOTH (CAS)
Text	8 ANSWER

How it's checked

4 test cases, each checked against an independent method. Replayed key by key on a virtual TI-89 Titanium, they make 59 checks.

How E-Code checks every program

Run it or put it on your calculator

Open the library in the TI-89 Titanium calculator and pick “Series RLC step response, step by step” (RLCSTEP).
Put it on your own calculator with a computer and a USB cable, or type it in by hand.

Related programs

All TI-89 Titanium engineering programs · All TI-89 Titanium programs