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?
angular frequency= sqrt(k/m)=w
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
which, according to the homework website, is not correct! Can anyone see where I made my mistake? Thank you!!