Physics

The displacement of a linear damped oscillator is given, for weak damping by
x=Ke^(-bΩt) sin⁡(βt+ ε)
Show x has a maximum at times given by βt = 2nπ + d where n is an integer and d is gives the position of the first maximum
Show also that the ratio of successive maxima is e^(2bΩπ/β).

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  1. maximum when sin(bt+e) = 1 or -1 but this seems only to look at the positive answer for max
    that is when argument = pi/2
    or pi/2 + n 2pi
    first max when pi/2
    so for first max
    b t(1) + e = pi/2 = d
    further maxes when
    b t(n) + e = d + 2 n pi
    so further max when b t/o = d + 2 n pi
    x max n = k e (-d+2pin)o
    xmax n+1 = k e^(-d +2 pi n +2 pi )o

    xmax n+1/xmax n = e^( - 2pi o)

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