Problem :
A mass of 2 kg is attached to a spring with constant 18 N/m. It is then displaced to the point x = 2 . How much time does it take for the block to travel to the point x = 1 ?
For this problem we use the sin and cosine equations we derived for simple harmonic motion. Recall that x = x mcos(σt) . We are given x and x m in the question, and must calculate σ before we can find t . We know, however, that no matter the initial displacement, σ = = = = 3 . Thus we can plug in our values:
= cosσt
= cos3t
3t = cos-1
t = = .35 seconds
This problem was a simple example of how to use our equations for simple harmonic motion.