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

At t = 0 a block with mass M = 5 kg moves with a velocity v = 2 m/s at position xo = -.33 m from the equilibrium position of the spring. The block is attached to a massless spring of spring constant k = 61.2 N/m and slides on a frictionless surface. At what time will the block next pass x = 0, the place where the spring is unstretched?

2. Relevant equations

phi=phase angle

angular frequency= sqrt(k/m)=w

x(t)=Acos(wt+phi)

3. The attempt at a solution

After working through the givens, I got my equation for the harmonic motion to be

x(t) = 0.66 cos (3.4987t - 2pi/3)

Where the angular frequency is sqrt(61.2/5)=3.4987, I got the amplitude from conservation of energy to be .6607 meters and the phase angle is -2pi/3.

The next step, if I am not mistaken, is to solve for when the spring is at its equilibrium position, or when x(t1)=0. Here are the steps for what I did...

0=0.6607 cos (3.4987t - 2pi/3)

0=cos(3.4987t - 2pi/3)

cos-1(0)=3.4987t - 2pi/3

pi/2= 3.4987t -2pi/3

7pi/6=3.4987t

t=1.0476 seconds

which, according to the homework website, is not correct! Can anyone see where I made my mistake? Thank you!!

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# Homework Help: Block and Spring (Simple Harmonic Motion Problem)

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