Simple Harmonic Motion: Calculate Max Velocity

AI Thread Summary
To calculate the maximum velocity of a mass in simple harmonic motion (SHM), the relevant parameters include the mass (0.4 kg), spring constant (k = 80 N/m), and amplitude (A = 0.10 m). The correct approach involves using energy conservation principles rather than uniform acceleration equations. At the equilibrium point, potential energy converts to kinetic energy, allowing the maximum speed to be determined. The correct maximum velocity is found to be 1.4 m/s, contrasting with the initial incorrect calculation of 2 m/s. Understanding the relationship between potential and kinetic energy is crucial for solving SHM problems effectively.
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Homework Statement


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.

Homework Equations


a = -kx/m
ω = 2pi/T

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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Use energy conservation.
 

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