Mechanics (1 Viewer)

[qna]

A couple of questions I had on mechanics:

1. What is n in the 2pi / n formula, and why is it always positive (apart from the fact that the period cannot be negative)
2. When writing max. velocity, why don't we use the plus-minus sign and just use the positive case?

 

[ShhQuietPlease]

I'm going to stab in the dark and assume this is simple harmonic motion. Let me know if it is not.

1. The SHM formula is . The formula you mentioned is for finding the period. In that formula, n is the number infront of x.
2. You are absolutely right that maximum velocity should be signed. However, in many cases, the question will ask for maximum speed where the sign is always positive.

 

[qna]

I'm going to stab in the dark and assume this is simple harmonic motion. Let me know if it is not.

1. The SHM formula is . The formula you mentioned is for finding the period. In that formula, n is the number infront of x.
2. You are absolutely right that maximum velocity should be signed. However, in many cases, the question will ask for maximum speed where the sign is always positive.

Yep this is SHM.

Is there like some sort of intuition behind what n is exactly? I've read in some places that it is angular velocity, but I'm not quite sure as to what that is.

And that makes sense, thank you!

 

[ShhQuietPlease]

Is there like some sort of intuition behind what n is exactly? I've read in some places that it is angular velocity, but I'm not quite sure as to what that is.

Definitely, lets come back to simple terms. What's period? We know the period is the time it takes for a particle to return back to its original position. It also happens that SHM are sin/cos curves. So the question is really how do we find the time it takes a sin/cos curve to return to its original position?

Let's visually compare and . We should notice that returns to the start position in seconds as opposed to which returns to the start position in seconds. This means intuitively, we know n has an impact on the period.

 

[Nav123]

Yep this is SHM.

Is there like some sort of intuition behind what n is exactly? I've read in some places that it is angular velocity, but I'm not quite sure as to what that is.

And that makes sense, thank you!

Adding onto that, n is the frequency. The frequency is basically how many times the wave repeats itself after 2pi seconds. So if n = 2 the wave repeats itself twice in 2pi seconds. If n =3 the period is 2pi/3 so the wave goes back to start every 2pi/3 seconds, hence in 2pi seconds the wave repeats itself 3 times.

If you did physics you might remember the formula period = 1/frequency, its the same concept here.

 

[qna]

Thank you!