Will the combination of 2 Simple Harmonic motions will be an SHM in itself? For example for simple functions such as
$$\ f(t)=\sin\omega t-\cos\omega t$$ I can use trigonometry to show that it can be expressed as $$\ f(t)=\sqrt 2\sin(\omega t-\pi/4) $$.
But what about functions given in the questions given below?
[Ref: “NCERT Class 11th (XI) Physics, Part 2”, Digital Designs; notes on p. 357 and Problem 14.4, p. 359 <link> ]
In (b) I can express the function as a combination of
$\sin\omega t$ and $\sin3\omega t$.
Each of these 2 terms can independently express an SHM but will their combination do the same?
As an answer to part (b) and (d) ,the book says that the superposition of two SHM is always periodic but never an SHM. (I believe that this is incorrect.Maybe a typo)
I am getting pretty confused.
Can anybody tell me when the combination of 2 SHM's be an SHM/periodic/not periodic?