A 4-foot spring measures 8 feet long after a mass weighing 8 pounds is attached to it. The medium through which the mass moves offers damping force numerically equal to the square root of two times the instantaneous velocity. Find the equation of motion if the mass is initially released from the equilibrium position with a downward velocity of 5 ft/s. After finding the time at which the mass attains its extreme displacement from the equilibrium position, what is the position of the mass at that instant?
Round in the hundredths place.

I don't even know.

Question

A 4-foot spring measures 8 feet long after a  mass weighing 8 pounds is attached to it.  The medium through which the mass moves offers damping force numerically equal to the square root of two times the instantaneous velocity.  Find the equation of motion if the mass is initially released from the equilibrium position with a downward velocity of 5 ft/s.  After finding the time at which the mass attains its extreme displacement from the equilibrium position, what is the position of the mass at that instant?
Round in the hundredths place.

I don't even know.

anonymous · Answer

Obviously it's a second order differential equation, but outside that I got nothing on this.

kira_yamato · Answer

Your differential equation will look in a form of
x'' + ax' + bx + c = 0
Where a, b, c are constants... I'll recommend the use of the complex plane