Math Questions (Simple Harmonic)

[StudyBuddyKJ]

Quick reminder please.

How do you calculate maximum velocity and maximum acceleration in SHM?

[RuiAce]

Just read off the amplitude from equations of the form \( a \sin (nt + \alpha) \) or \( a \cos (nt + \alpha) \).

[jamonwindeyer]

Quick reminder please.

How do you calculate maximum velocity and maximum acceleration in SHM?

And to expand on above, you then substitute the amplitude into the relevant equations! Remembering:

- Velocity is maximised at the centre of motion
- Acceleration is maximised at the endpoints of motion

So, when \(x=a\), you have maximum acceleration. When \(x=b\) (the centre, possibly the origin), then you have maximum velocity

[StudyBuddyKJ]

These questions are so easy, but I'm finding simple harmonic motion so hard to understand. My test is in two days, please help!

[RuiAce]

These questions are so easy, but I'm finding simple harmonic motion so hard to understand. My test is in two days, please help!

You should have been taught the formula \( v^2 = n^2 (a^2 - x^2) \) in class. That equation holds when the equilibrium point is 0. Otherwise, \(x_0\) represents the equilibrium point.

[StudyBuddyKJ]

What

You should have been taught the formula \( v^2 = n^2 (a^2 - x^2) \) in class. That equation holds when the equilibrium point is 0. Otherwise, \(x_0\) represents the equilibrium point.

What do you mean by equilibrium point?

[RuiAce]

What
What do you mean by equilibrium point?

The equilibrium point is just (a fancy name for) the centre of motion. In SHM, a particle is always going back and forth from a central point.