A mass weighing 6 pounds stretches a spring 2 feet. The mass is attached to a dashpot device that offers a damping force numerically equal to β (β > 0) times the instantaneous velocity. Determine the values of the damping constant β so that the subsequent motion is overdamped, critically damped, and underdamped. (If an answer is an interval, use interval notation. Use g = 32 ft/s2 for the acceleration due to gravity.)

Astone is thrown into a pond. what happens to the amplitude of the resulting waves as they get farther from the point where the stone hit the water? explain.

Identify the correct relation showing that the radius r of the orbit of a moon of a given planet can be determined from the radius r of the planet, the acceleration of gravity at the surface of the planet, and the time τ required by the moon to complete one full revolution about the planet. determine the acceleration of gravity at the surface of the planet jupiter knowing that r = 71 492 km and that t= 3.551 days and r= 670.9 × 10^3 km for its moon europa.

Aturntable that spins at a constant 74.0 rpm takes 3.10 s to reach this angular speed after it is turned on. find its angular acceleration (in rad/s2), assuming it to be constant, and the number of degrees it turns through while speeding up.