from sympy import *
from spb import *
x, a, b, c, n = symbols("x, a, b, c, n")
plot(
    (cos(a * x + b) * exp(-c * x), "oscillator"),
    (exp(-c * x), "upper limit", {"linestyle": ":"}),
    (-exp(-c * x), "lower limit", {"linestyle": ":"}),
    prange(x, 0, n * pi),
    params={
        a: (1, 0, 10),     # frequency
        b: (0, 0, 2 * pi), # phase
        c: (0.25, 0, 1),   # damping
        n: (2, 0, 4)       # multiple of pi
    },
    ylim=(-1.25, 1.25),
    title=("Frequency = {:.2f} Hz", a)
)