Expression 7: "f" left parenthesis, "t" , right parenthesis equals sine left parenthesis, omega Subscript, "v" , Baseline left parenthesis, "t" , right parenthesis times "t" , right parenthesisft=sinωvt·t
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A correct way of modelling a changing ω that yields the desired behavior
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Expression 9: "f" left parenthesis, "t" , right parenthesis equals sine left parenthesis, Start integral from 0 to "t" , end integral, omega Subscript, "v" , Baseline left parenthesis, "x" , right parenthesis "d" "x" , right parenthesisft=sin∫t0ωvxdx
9
Constants to control the variable ω function. a is the t value for the start of the ramp, b is the t value for the end of the ramp, ω1 is the initial value of ω, and ω2 is the final value of ω.