physics
posted by Emily .
A 2.24 kg mass on a frictionless horizontal track is attached to the end of a horizontal spring whose force constant is 4.45 N/m. The mass is displaced 3.06 m to the right from its equilibrium position and then released, which initiates simple harmonic motion. How many times does the mass oscillate in 24.2 s?

First, find the equations that are pertinent to the problem.
F(spring) = k*x
where F(spring) is the force on a spring, k is the spring constant, and x is the displacement.
w = (k/m)^1/2
where w is the angular acceleration, m is the mass of the spring
T = 2*PI/w
where T is the period of oscillation
w = (4.45/2.24)^0.5
T = 2*PI/w
The number of times the mass will oscillate in 24.2 s is 24.2/T