1. A mass weighing 10 lbs. is attached to a spring suspendedfrom the ceiling. The mass will stretch the spring 6 inches. If themass is pulled 5 inches below its equilibrium point and given aninitial upward velocity of 0.3 ft./sec. and if damping forces areneglected, then what is the equation of motion of the mass? What isthe amplitude of the motion?
2. A 980-newton force stretches a spring 0.4 meters. If a 200 kgmass is attached to the spring and pulled 0.5 meters below itsequilibrium point and released, neglecting damping forces, what isthe equation of motion of the mass?
3. A mass weighing 8.2 pounds will stretch this spring 1.36feet. The spring/mass system is damped by a force that is 1.5 timesthe instantaneous velocity of the mass. Determine the equation ofmotion of the mass, if the mass is stretched 1 foot below itsequilibrium point and released.
4. A 1 newton force will stretch a spring 1 meter. Thespring/mass system is damped by a force that is 8 times theinstantaneous velocity. A 12 kg mass is attached to the spring. Thespring is compressed 0.8 meters above the equilibrium position andgiven an initial downward velocity of 3 m/s. Determine the equationof motion of the mass
5. A mass weighing 3(1/5) pounds stretches a spring by 1 foot.If the spring/mass system is damped by a force that is twice theinstantaneous velocity and this same mass is given an initialupward velocity of 1.3 ft/sec from the equilibrium position, thenwhat is the equation of motion of the mass?
