Exponential Function (L2-13 to L2-16)
This demo describes the complex exponential function as described on pages L2-13 to L2-16 in the script. The complex time function is described by \(x(t)=\hat{X}\cdot \mathrm e^{st}\) with the complex frequency \(s=\sigma+\mathrm{j}\omega\). The amplitude \(|\hat{X}|\), the angular frequency \(\omega\), the damping \(\sigma\) and a phase shift \(\varphi\) can be set. The following applies: \(\hat{X} = |\hat{X}|\cdot \mathrm e^{\mathrm{j}\cdot\varphi}\)
Magnitude \(|\hat X|\)
1.0
Phase \(\varphi\) [rad]
0.0
Real part \(\sigma\)
0.2
Frequency \(\omega\)
3.0
Time \(t\)
6.0
Mode