5. A mass of 5 kg is attached to a spring with a spring constant k=20 N/m. The damping constant c=10 Ns/m provides resistance proportional to the velocity of the mass. The system is displaced 0.2 meters from equilibrium and released from rest. (a) Set up the differential equation that models the motion of the mass. (b) Solve the equation to find the displacement y(t) as a function of time. (c) What is the natural frequency and the actual oscillating frequency of this vibration system?

Don't skip the steps, Write the equations clearly in step by step.

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6) An inverted open tank is held in place by a force R as shown in figure. If the specific gravity of the manometer fluid is 2.5, determine the value of h and R. Neglect the weight of the tank. 1 cm diameter tube R 2 m diameter tank h Air 13 m 2 m Water 1 m Water

(3) Consider the force F(t) acting on the spring-mass system shown. Determine the steady-state response to this forcing function. K = 1000 N/m F(t) A 100 10 kg F(t) -100 C=0.5 kg/s 1 2

Derive the equation of motion of the weight w suspended from a spring at the free end of the cantilever steel beam shown below. For the steel, E = 200x10°mpa. Ignore the mass of beam and spring 3.0m 50mm diameter steel rod k = 3572N/m M =100kg P(t) Exercige 2

A force of 13 pounds stretches a spring 1 foot. A mass weighing 6.4 pounds is attached to the spring, and the system is then immersed in a medium that offers a damping force numerically equal to 1.6 times the instantaneous velocity. (a) Find the equation of motion if the mass is initially released from rest from a point 1 foot above the equilibrium position. x(t) = ft (b) Express the equation of motion in the form x(t) = Ae-t sin(√² - 1²t + p), which is given in (23) of Section 3.8. (Round to two decimal places.) x(t) = ft (c) Find the first time at which the mass passes through the equilibrium position heading upward. (Round your answer to three decimal places.)

The mass center G of the 1505-kg rear-engine car is located as shown in the figure. Determine the normal force under each tire when the car is in equilibrium. State any assumptions. Answers: -1298 mm-891 mm- Normal force under each of the front tires: N₁= Normal force under each of the rear tires: Tel N₁ = i N N

The mechanism used in a marine engine consists of a single crank AB and two connecting rods BC and BD as shown in (Figure 1). Assume r = 0.1 m. Figure Da 0.4 m 60° B 30° @ 0.4 m 45° 1 of 1 Part A Determine the magnitude of the velocity of the piston at C the instant the crank is in the position shown and has an angular velocity of 8 rad/s. Express your answer to three significant figures and include the appropriate units. VC = Submit Part B 0 μA Value Submit Request Answer up and to the right Determine the direction of the velocity of the piston at C the instant the crank is in the position shown and has an angular velocity of 8 rad/s. down and to the left Completed Previous Answers Units Return to Assignment ? Provide Feedback

Problem 10.96 The pendulum consists of a disk having a mass of 7 kg and slender rods AB and AC which have a mass of 2 kg/m. (Figure 1) Figure 1 0.2 m A of 1 0.8 m 0.5 m-D B Part A Determine the length L of DC so that the center of the mass is at the bearing O. Express your answer to three significant figures and include the appropriate units. L = Submit Io = μA Submit Value My Answers Give Up Part B What is the moment of inertia of the assembly about an axis perpendicular to the page and passing through point O? Express your answer to three significant figures and include the appropriate units. Units μA Value Units ? My Answers Give Up ?