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 its

subsequent motion is given by

*mz'' *+ *kz *= 0*.*

*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 the

mass is now given by

2z''+ 4*z'* + 4*z *= 0

My working: what is the constant of proportionality?

* *