(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

This was a question on my 2nd midterm that I am still curious about.

An unusual spring has a force law given by F = -cx^3 where x is in meters, F is in Newton's, and c has units of N/m^3.

The spring is used to launch a 3.00 kg block across a horizontal frictionless surface. If c = 600 N/m^3 and the spring is initially compressed by 0.500 m, what will the velocity of the block be when it reaches the equilibrium position?

2. Relevant equations

F = ma

x(t) = Acos(ωt)

v(t) = -Aωsin(ωt)

a(t) = -A(ω^2)cos(ωt)

3. The attempt at a solution

First, I find the acceleration with the equation ma = -cx^3 (with the direction positive to the left of the equilibrium position) during initial position because that is where maximum acceleration occurs. I get a value of a = -25m/s^2.

I plug this into the a(t) = -A(ω^2)cos(ωt) with t = 0, and I get a value of ω = 7.071.

Now since I have ω, I can use v(t) = -Aωsin(1) to find maximum speed which occurs at the equilibrium position. I get an answer of 3.54 m/s, which fits into one of the multiple choice questions.

The problem is that the actual answer is 2.50 m/s, and I have no idea what else I can do to solve this.

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# Homework Help: SHM with unusual spring

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