SHM: Equation relating acceleration and displacement

1. Mar 24, 2015

andyrk

A particle moves such that its acceleration is given by: a = -β(x-2). Here β is a positive constant and c is the distance from origin What is the time period of oscillation for the particle?

Solution: a = 0 at x = 2 (mean position)
a = -βX where X = x-2.
So, ω2 = β ⇒ T = 2π/ω = 2π/√β

My question is, why do we need to substitute x-2 as X? Can't we solve the problem without doing this?

2. Mar 24, 2015

BruceW

you can do the whole problem without the substitution. I guess that using the substitution means that you can immediately recognise that the problem is SHM.

3. Mar 24, 2015

andyrk

So then, would we call x-2 as the distance from the mean position or x?

4. Mar 24, 2015

andyrk

There's not much depth involved in this. I am overthinking things.

5. Mar 25, 2015

BruceW

yeah :) x-2 is the displacement from the equilibrium position, which makes it a convenient choice to use as coordinate, instead of using x.

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