12 questions linked to/from Explanation: Simple Harmonic Motion
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### Check whether the expression shows periodic motion or simple harmonic motion [duplicate]

How can you check whether the given expression shows simple harmonic motion or not?And also how to calculate angular frequency of the given equation?
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### Why do we use sine/cosines in Simple Harmonic Motion? [duplicate]

For example, to calculate the displacement of the particle in an harmonic oscillator we do: $$x(t) = x_{\max} \cos(ωt+φ)$$ What do we find out taking the cosine of (ωt+φ)? Example Graph:
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### Simple harmonic motion equation [duplicate]

I don't really understand this equation and was wondering if someone could help. The book says when the restoring force is directly proportional to the displacement the oscillation is called SHM. ...
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### Conceptual question about Osillations [duplicate]

I am confused about simple harmonic motion. I understand that it follows a sine wave but is it possible to explain why it does?
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### How to derive the period of spring pendulum?

So I wanted to find out how to (simply, if that's possible) derive the formula for a period of spring pendulum: $T=2\pi \sqrt{\frac{m}{k}}$. However, Google doesn't help me here as all I see is the ...
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### How to prove that a motion is Simple Harmonic Motion (SHM)?

I would like to know how one could show and prove that a given motion is simple harmonic motion. Once given an answer, I'll apply that technique to an example I am trying to figure out. Thank you ...
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### Spring pendulum - why is it possible to use this equation?

It is known that, when we describe the spring pendulum, we are bound to use the formula $T = 2\pi \sqrt{m/k}$, however, we can go further and set $\omega = \frac{2\pi}{T}$ I ponder why is this ...
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 ...