Question

In problems 14-17, set up the spring mass equation. Determine whether it is undamped, under, critically or overdamped. Solve the IVP and draw a graph (technology is cool) of the solution on the interval 0 < t < 12. If the system Is underdamped convert the solution to the form Re^alpha t sin(beta t + delta) A mass weighing 64 pounds stretches a spring 0.32 foot. The mass is initially released from a point 8 inches above the equilibrium position with a downward velocity of 5 ft/sec. A force of 400 N stretches a spring 2 meters. A mass of 50 kg is attached to the end of the spring and initially released from the equilibrium position with an upward velocity of 10 m/sec A mass weighing 4 lbs. is attached to a spring whose constant is 2lb./ft. The medium offers a ping force that is numerically equal to the instantaneous velocity. The mass is initially released from a point 1 foot above the equilibrium positon with downward velocity of 8 ft./sec

Answer 1

For damped osellalkos ,thi equalian iven by b-> damping conslant 1k-realo fore O b -20 am Nous From data de84t/sec d t e eneral Solobon am たA1 e

2m2x4.IS i e -o-125 t 0-125 h => A)に 1 dcbberenhala genS oeget -0-12S t 0 0868

A12-14 tan δ= A2一-92-16 A, o-tani (-92-16)--89.31 E9n⑤ beco me - o 12s t tsin -O-12st -0012s t O-12S

70- 60 50 40 30 10 ←-10 -20 -30 -40 -50 -60 -70 -80 0 1 2 3 45 6 7 8 9 10 11 12 13 t in sec

graph plotted in origin lab, using above equation