91Ó°ÊÓ

A spring is such that it is stretched 6 in. by a \(12-1 \mathrm{~b}\) weight. The \(12-\mathrm{lb}\) weight is pulled down 3 in. below the equilibrium point and then released. If there is an impressed force of magnitude \(9 \sin 4 t\) lb, describe the motion. Assume that the impressed force acts downward for very small \(t\).

A spring is stretched 10 in. by a 4-lb weight. The weight is started 6 in. below the equilibrium point with an upward velocity of \(8 \mathrm{ft} / \mathrm{sec} .\) If a resisting medium furnishes a retarding force of magnitude \(\frac{1}{4}|v|,\) describe the motion.

A spring is such that a 2 -lb weight stretches it \(\frac{1}{2} \mathrm{ft}\). An impressed force \(\frac{1}{4} \sin 8 t\) is acting upon the spring. If the 2 -lb weight is released from a point 3 in. below the equilibrium point, determine the equation of motion.

A spring is stretched 4 in. by a 2-lb weight. The 2 -lb weight is started from the equilibrium point with a downward velocity of \(12 \mathrm{ft} / \mathrm{sec} .\) If air resistance furnishes a retarding force of magnitude 0.02 of the velocity, describe the motion.

A spring is such that a 16 -lb weight stretches it 1.5 in. The weight is pulled down to a point 4 in. below the equilibrium point and given an initial downward velocity of \(4 \mathrm{ft} / \mathrm{sec} .\) An impressed force of \(360 \cos 4 t \mathrm{lb}\) is applied. Find the position and velocity of the weight at time \(t=\pi / 8\) sec.

A spring is such that it is stretched 4 in. by a 10 -lb weight. Suppose the 10 -lb weight to be pulled down 5 in. below \(E\) and then given a downward velocity of \(15 \mathrm{ft} / \mathrm{sec}\). Describe the motion.

A spring is such that a 4 lb weight stretches it 6 in. The 4 -lb weight is attached to the vertical spring and reaches its equilibrium point. The weight is then \((t=0)\) drawn downward 3 in. and released. There is a simple harmonic exterior force equal to \(\sin 8 t\) impressed upon the whole system. Find the time for each of the first four stops following \(t=0 .\) Put the stops in chronological order.