- #1

kmsiva

- 2

- 0

## Homework Statement

Hi,[/B]

I am trying to get an envelope function for two sinusoidal curves (A, B) added up.

a1,a2 are the amplitudes(metre), T1,T2 are the periods (hrs), B lags by dt from A at t=0.

case-1:

a1= 1, a2=0.5, p1=11,p2=10,dt=0

w1=2*pi/T1,w2=2*pi/T2

A = a1*cos(w1*t), B=a2*cos(w2*t+dt)

t varies from 0 to 650 hours

## Homework Equations

Case-1[/B]

using a envelope function sqrt(a1^2 + a2^2+2*a1*a2*(cos(w2-w1)*t+dt))

i am getting a nice envelope as in the figure 1

**Case-2:**

a1= 1, a2=0.5, T1=60, T2=10, dt=0

using a envelope function

a2 – a1 +2*a1*a2*(cos(w1)*t+dt))

I can manage an envelope as in the figure 2

## The Attempt at a Solution

Is there a way to combine these two conditions ( or any combination of T1 and T2)

so that I can have one generalized envelope function that does not miss the peaks.

Thanks in anticipation for any help