If the mass is displaced from its equilibrium position by a distance x a force F will act in the opposite direction to the displacement. Examples of SHM Spring Mass SystemĬonsider a spring of spring constant k conected to a mass m. Thus the maximum acceleration is ±ω 2 A which occurs at the ends of the oscillations, as this is where the direction changes. The maximum acceleration occurs where the argument of cosine in eqn (7) is also -1 or 1. The minus sign indicates the direction of travel is in the opposite direction. Intuitively, we can imagine that this velocity occurs when the oscillating system has reached the equilibrium position and is about to overshoot. From equation (6) the maximum magnitude of the velocity occurs when sin(ωt - φ) is 1 or -1. The time for the maximum velocity and acceleration can be determined from these equations. With the constant of proportionality k = ω 2 Substituting equations (5) and (7) into equation (4) we verify that this does indeed satisfy the equation for simple harmonic motion.
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |