Spring aproximation

[phy_magic]

Homework Statement

About a steel wire of length l=6m and cross-section A=0.5mm2, the height of a metal ball of mass m=2kg. If the ball is lifted to a height h and then released, it will start to oscillate in the vertical direction.
a) What is the character of these oscillations for different heights h?
b) For what amplitudes will the oscillations be sinusoidal?
c) Determine the period of sinusoidal oscillations.

Relevant Equations

Young modul, stress in wire

What should be good aproximation for amplitides?
So I started with calculatin k for this wire from hooke law and young modul , and I use statement that "spring" folows hooke law only in some region of elongation. If i want oscilation to be sinusiondal is that condition that hooke law is correct in that region of elogation

 

[Chestermiller]

Homework Statement: About a steel wire of length l=6m and cross-section A=0.5mm2, the height of a metal ball of mass m=2kg. If the ball is lifted to a height h and then released, it will start to oscillate in the vertical direction.
a) What is the character of these oscillations for different heights h?
b) For what amplitudes will the oscillations be sinusoidal?
c) Determine the period of sinusoidal oscillations.
Relevant Equations: Young modul, stress in wire

What should be good aproximation for amplitides?
So I started with calculatin k for this wire from hooke law and young modul , and I use statement that "spring" folows hooke law only in some region of elongation. If i want oscilation to be sinusiondal is that condition that hooke law is correct in that region of elogation

Yes, neglecting dissipation factors such as air drag.

 

[phy_magic]

what should be condition while calculating that value of amplitude , if we neglect dissipation of any kind, like oreder of magnitude od dl /l or σelastic limit

 

[Steve4Physics]

what should be condition while calculating that value of amplitude , if we neglect dissipation of any kind, like oreder of magnitude od dl /l or σelastic limit

SHM requires that the restoring force is proportional to the displacement from the equilibrium position.

Find the limit of proportionality (sometimes called the proportional limit) for steel. The maximum amplitude for SHM corresponds to the steel stretched to to this limit.