How do I shift this function to the right by 1?

Question

I have the function:

$$y =13000e^{-0.075t}cos\left(\frac{2πt}{4}\right) | 0\le{t}\le{20}$$

Which creates the graph:

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.

What I need the graph to look like

I have just tried $$y =13000e^{-0.075t}cos\left(\frac{2π(t-1)}{4}\right) | 0\le{t}\le{20}$$ however the peak is now 12074 rather than 13000. — david_10001, Jun 01 '18 at 01:35
You need to change t in exponent of e too, also the domain changes — mateeeeeee, Jun 01 '18 at 01:43

score 1 · Accepted Answer · answered Jun 01 '18 at 01:52

1

Try, $$13000e^{-0.075(t-1)}cos\left(\frac{2π(t-1)}{4}\right) , 0\le{t}\le{20}$$

answered Jun 01 '18 at 01:52

Mohammad Riazi-Kermani

68,728

Thank you, this works – david_10001 Jun 01 '18 at 02:12

How do I shift this function to the right by 1?

1 Answers1