How to express the following equation into a sine wave equation ?
$$S(t) = 4 + 3 \sin 100 \pi t + 5 \sin 200 \pi t$$
I understand that, for the sine wave with same frequency and different amplitude,
I can use the formula
$$\sin (\omega t)+ A_{2}\sin (\omega t)=(A_{1}+A_{2})\sin (\omega t)$$
but how to add sine wave that has different frequency ?
Thanks!
You can't add two sines of different frequencies. This is a fundamental limit which much of math and physics takes advantage of.
Its also the basis of the fourier transform.
To put it simply, sines of different frequencies are orthogonal.