Use the following information for problems 68 A mass weighin

Use the following information for problems 6-8: A mass weighing 16 lb stretches a spring 1 feet. The mass is initially released from rest at a point 1 feet below the equilibrium. a) Find the equation of motion with no damping b) Graph the equation of motion of the mass 6.

Solution

Forces on mass

1)F_spring = -kx                     (where x is the expansion or suspension in the spring)

2)F_gravity = mg (downward)

net force = F_spring + Fgravity = mg - kx = ma

hence a = dv/dt = g-(k/m)x

hence d(dx/dt)/dt = d²x/dt² = g-(k/m)x            (as v = dx/dt)

it is 2nd order differential equation in x and t