# Simple Harmonic Motion: Calculate Max Velocity

**1. The problem statement, all variables and given/known data**

A mass of 0.4 kg, hanging from a spring (k= 80N/m) is set into an up-and-down SHM. What is the speed of the mass when moving through the equilibrium point? The starting displacement, A, is 0.10 m.

**2. Relevant equations**

a = -kx/m

ω = 2pi/T

**3. The attempt at a solution**

I tried to apply one of the equations of motion: 2ax = vf^2 – vi^2: but I got an answer of 2 m/s, which is incorrect as the correct answer is 1.4 m/s. Now, I realize that acceleration is not uniform which means that I can’t use that equation.

However, I’m not sure what else to do. Using a = -kx/m I managed to calculate the acceleration at the equilibrium point, but without any sort of time or time period or frequency, I haven’t a clue how to solve this question.

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