ex.) An object weighing 128 pounds is suspended from a spring, stretching the spring 2 feet beyond its natural length. The weight is then released from rest at a point 6 inches above the equilibrium position.
a.) Find the function describing its position at time t.
Answer:
128=k(2)=>256
m=4 slug
4x"+256x=0
I use this formula: W= sqrt 256/4 = sqrt 64 = 8
u(0)= -4, because spring is going in reverse (above)
u'(0)= 0
I am a bit unsure what to do when the velocity isnt given in the problem.
u(t)= c1 cos (8t) + c2 sin (8t)
u'(t)= -8c1 sin (8t) + 8c2 cos (8t)
Apply initial conditions: -4 = u(0) = c1 => c1 = -4
0 = u'(0)= 8c2 cos (8t) => c2=0 ?
u(t)= -4cos (8t) + sin (8t)
a.) Find the function describing its position at time t.
Answer:
128=k(2)=>256
m=4 slug
4x"+256x=0
I use this formula: W= sqrt 256/4 = sqrt 64 = 8
u(0)= -4, because spring is going in reverse (above)
u'(0)= 0
I am a bit unsure what to do when the velocity isnt given in the problem.
u(t)= c1 cos (8t) + c2 sin (8t)
u'(t)= -8c1 sin (8t) + 8c2 cos (8t)
Apply initial conditions: -4 = u(0) = c1 => c1 = -4
0 = u'(0)= 8c2 cos (8t) => c2=0 ?
u(t)= -4cos (8t) + sin (8t)