I have the function:
$$y =13000e^{-0.075t}cos\left(\frac{2πt}{4}\right) | 0\le{t}\le{20}$$
Which creates the graph:
What graphs currently looks like
At the moment the largest y value is 13000, starting at t = 0 However it is meant to peak at t = 1 like in the bottom figure. I have tried the following:
$$y =13000e^{-0.075t}cos\left(\frac{2πt}{4}+1\right) | 0\le{t}\le{20}$$ $$y =13000e^{-0.075t}cos\left(\frac{2πt}{4}+2\right) | 0\le{t}\le{20}$$ $$y =13000e^{-0.075t}cos\left(\frac{2πt}{4}+t\right) | 0\le{t}\le{20}$$ $$y =13000e^{-0.075t}cos\left(\frac{2πt}{4}+2t\right) | 0\le{t}\le{20}$$ $$y =13000e^{-0.075t}cos\left(\frac{2πt}{4}+π\right) | 0\le{t}\le{20}$$ $$y =13000e^{-0.075t}cos\left(\frac{2πt}{4}+2π\right) | 0\le{t}\le{20}$$
Plus all the above except subtracting the values. Nothing has been able to correctly shift it so the graph looks like that below.
Try, $$13000e^{-0.075(t-1)}cos\left(\frac{2π(t-1)}{4}\right) , 0\le{t}\le{20}$$