An object of mass m is suspended from a vertical spring of force constant 1800 N/m. When the object is pulled down 2.50 cm from equilibrium and released from rest, the object oscillates at 5.500 Hz. a) Find m, b) Find the amount the spring is stretched from its unstressed length when the object is in equilibrium, c) Write expressions for the displacement x, the velocity v and the acceleration a as functions of time t.
For simple harmonic motion, we have that
x=A*cos(ωt + δ), where δ is the phase constant.
The Attempt at a Solution
For this particular problem, I am only concerned with c), and moreover finding the phase constant δ. Actually, not finding it, but to understand why it should exist in the first place, i.e., a non-zero phase constant (we can find it by solving the equation set x=A*cos(ωt + δ) and v=-ωA*sin(ωt + δ) for δ).
I gather that if a particle or an object is released from rest, that x=A, hence δ=0, which to me makes the most sense by looking at an x/t graph, seeing that it's at its greatest value at t=0, so there can be no phase shift. My intuition tells me that the same thing should apply to an object hanging from a spring. But since apparently it doesn't, I am led to think that gravity can cause the object to move past the initial point x, to which the spring is elongated, as there is seemingly no other explanation for this. As a matter of fact, this is the only reason I can think of, and it's the only thing that's different from a situation in which a spring is being pulled horizontally. Yet still, this difference isn't mentioned in the book, so I would appreciate someone explain this to me.