how to plot Integrate of exponent and cosine equation.

i want to do simulation to plot this equation;

where i want to change the phi with 0, π/4, and π/2.

Next, I want to do,

where i want to see what is the shape of the graph with multiple tau is used.

Can anyone help me some idea how to start? i appreciate it so much!

[darova]

Can you describe other parameters? What are they? Scalars? COnstants? Vectors?

[Shubham Gupta]

Where is tau in the 2nd equation? and what is 'T' in both the equations?

[Hafizah Halip]

these are the parameter

Here, α is the initial fluorescence intensity emitted by the sample when irradiated by laser pulses; τ is the fluorescence lifetime; ω denotes the repetition angular frequency of the short-pulsed laser; T is the period of pulse repetition (T = 2π/ω); φ is the phase difference between the excitation pulse sequence and reference signal of the lock-in amplifier.

freq = 80MhHz

T = 1/f

for equation 2, tau is τ 1 and τ 2

[darova]

What are τ 1 and τ 2 ? Are they numbers?

[Hafizah Halip]

yes.

lets say

T1= 2ns

T2 =4ns

Answer 1

[Martin C.]

you can try something like this

syms tau t
f = exp(-t/tau).*cos(t+1)
func = int(f,t,0,1)
x = 0.01:.01:10;
y = subs(func, x)
plot(x,y)