by HallsofIvy » Fri Feb 14, 2020 1:02 pm
If both machines are switched on the two machines will produce a wave which will, at some time, reach a maximum. That is completely different from asking when each machine will produce a maximum! Also, there is no variable, "t" in your functions were they supposed to be
x1=5sin(100t+π/2)
x2=6.5sin(100t-π/3)?
If so, then the first is maximum when 100t+ π/2= nπ/2, for integer n, so 100t= (n-1)π/2 so t= (n-1)π/200. The second is maximum when 100t- π/3= nπ/2 so 100t= nπ/2- π/3= (3n- 2)π/6 so t= (3n- 2)π/600.
But I suspect your real question is about the maximum of the sum of these two functions, not the maximum of each. You will need to use sum and difference trig formulas.
If [b]both[/b] machines are switched on the two machines will produce a wave which will, at some time, reach a maximum. That is completely different from asking when [b]each[/b] machine will produce a maximum! Also, there is no variable, "t" in your functions were they supposed to be
x1=5sin(100t+π/2)
x2=6.5sin(100t-π/3)?
If so, then the first is maximum when 100t+ π/2= nπ/2, for integer n, so 100t= (n-1)π/2 so t= (n-1)π/200. The second is maximum when 100t- π/3= nπ/2 so 100t= nπ/2- π/3= (3n- 2)π/6 so t= (3n- 2)π/600.
But I suspect your real question is about the maximum of the sum of these two functions, not the maximum of [b]each[/b]. You will need to use sum and difference trig formulas.