A spring-mass system has a spring constant of 3 N/m. A mass of 2 kg is attached to the spring, and the motion takes place in a viscous fluid that offers a resistance numerically equal to the magnitude of the instantaneous velocity. If the system is driven by an external force of (21 cos 3t − 14 sin 3t) N, determine the steady state response. Express your answer in the form R cos(ωt − δ). (Let u(t) be the displacement of the mass from its equilibrium position at time t.)

What is the speed of an object at a given moment?

To understand the behavior of the electric field at the surface of a conductor, and its relationship to surface charge on the conductor. a conductor is placed in an external electrostatic field. the external field is uniform before the conductor is placed within it. the conductor is completely isolated from any source of current or charge. part a: which of the following describes the electric field inside this conductor? it is in the same direction as the original external field. it is in the opposite direction from that of the original external field. it has a direction determined entirely by the charge on its surface. it is always zero. part b: the charge density inside the conductor is: 0non-zero; but uniformnon-zero; non-uniforminfinite part c: assume that at some point just outside the surface of the conductor, the electric field has magnitude e and is directed toward the surface of the conductor. what is the charge density η on the surface of the conductor at that point? express your answer in terms of e and ϵ0

Amass weighing 24 pounds, attached to the end of a spring, stretches it 4 inches. initially, the mass is released from rest from a point 8 inches below the equilibrium position. find the equation of motion. (use g = 32 ft/s2 for the acceleration due to gravity.)