Answer:
∆x = A / √2
Explanation:
If the mass is oscillating in a SHM, the total mechanical energy at any time is given by the following equation:
½ k A2 = ½ k (∆x)2 + ½ mv2
We are told that at the point that we are looking for, the elestic potential energy, and the kinetic energy, are equal each other.
As we have no information regarding kinetic energy, we can replace it with the equivalent in potential energy, so we have:
½ k (∆x)2 + ½ mv2 = 2 (1/2) k (∆x)2 = k (∆x)2
We know that this energy must be equal to ½ k A2, so we can put the following:
½ k A2 = k (∆x)2
Simplifying common terms, and solving for the displacement from the equilibrium point (∆x), we get:
∆x = A / √2
Explanation:
