A spring is such that a 2-lb weight stretches it 6 inches. There is a damping force present, with magnitude the same as the magnitude of the velocity. An impressed force (2sin8t) is acting on the spring. If at t = 0, the weight is released from a point of 3 inches below the equilibrium point, find its position for t > 0.

2 - A particle is subjected simultaneously to two SHMS of the same frequency and in the same direction. If their amplitudes are 1.5 mm and 2.5 mm respectively and the phase of the second component relative to the first is 40°, find the amplitude of the resultant displacement and its phase relative to the first SHM.

4. A mass-spring system exhibits a period of 5 s and a measured mass of 20 kg. Calculate the spring stiffness k.

2. For the system below: a. Give an equation of motion for h. Note that the system has two inputs, p1 and p2. b. When h= 5, give the force exerted on the bottom of the tank. (Assume that the width and height of the opening at the bottom of the tank is negligible. The area of the bottom of the tank is A). h PA PI P2 PA R

Two box hang from the ends of a string suspended from a frictionless pulley. The mass on the left is chosen to create a tension of 4 N in the string. The box on the right has a weight of 2 N. What will be the acceleration of the box on the right? Assume the acceleration of gravity is 9.8 m/s?. 4 N 2 N

Solve step by step in digital form

Under some circumstances when two parallel springs, with constants k₁ and k2, support a single mass, the effective spring constant of the system is given by k = 4k1k₂/(k₁ + k₂). A mass weighing 20 pounds stretches one spring 4 inches and another spring 2 inches. The springs are attached to a common rigid support and then to a metal plate. As shown in the figure, the mass is attached to the center of the plate in the double-spring arrangement. k₂ II k = 20 lb Determine the effective spring constant of this system. lb/ft Find the equation of motion x(t) if the mass is initially released from the equilibrium position with a downward velocity of 6 ft/s. (Use g for the acceleration due to gravity.) 32 ft/s² x(t) = ft