A particle of mass
m is suspended from a ceiling by a spring of natural length l and
stiffness k. Assume that there is no damping
If the mass is displaced from equilibrium show that the equation governing itsmz'' + kz = 0.
subsequent motion is given by
My working:If we let e be the extension then N2L is ke-mg=0 so ke=mg.
An engineer measures the mass of the particle to be
m = 2, and furthermore k = 4.
He also finds that internal friction in the spring provides damping that is proportional
to the velocity of the particle with a constant of proportionality μ = 4.
Show that the equation for the subsequent motion after the displacement of the2z''+ 4z' + 4z = 0
mass is now given by
My working: what is the constant of proportionality?