By applying Newton second low to spring - mass -pulley as shown in the figure. Obtain the motion of mass m when it is pulled down a short distance and then released. The displacement x of a hanging mass m is measured from equillibrium position. (The mass, the radius and the moment of ineria of the pully are, m and repectively). x 7 R M k 8

vibrations, show all steps and solution

vibrations, show all steps and solutions

Find the equation of motion of the following spring system.

Sphere, mass m 000 Q4: Find the equivalent stiffness and mass of the system shown in the figure, then find the natural frequency. No slip Bell crank lever.- mass moment of inertia Jo 90° k₁ m 00000 TTTTTTT x(t)

4. A student followed strictly correct procedure in the lab during the experiment of moment of inertia. He measured the mass and diameter of plastic cylinder with value of m = 0.36 kg and D = 0.1 m. The period of system without plastic cylinder is To = 0.667 s. The period of system with plastic cylinder T₁ = 0.92 s. Find: The spring constant K of the system. If a metallic cylinder and a plastic cylinder have same diameter and same thickness, which one has larger moment of inertia? Explain.

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I Review Use a block-and-spring model like that shown in the figure, but suspended from a vertical position and subjected to a periodic support displacement 8 = 8psinwnt, determine Express your answer as an equation in terms of some or all of the variables y, a (a = y), ki, m, wn (wn = V). wn, t, and on. the equation of motion for the system, and obtain its general solution. Assume positive displacement is downward. (Figure 1) Va AZo| t vec k la+ m k sin @, t m That's not quite right. Please check your formatting and try again. No credit lost. Try again. Submit Previous Answers Request Answer Part B Obtain the general solution of the above equation. Figure 1 of 1 Express your answer in terms of some or all of the variables A, B, t, k, m, wn (Wn = 1/), 80, and wo. V ΑΣφ vec Equilibrium position A sin (@,1) +B cos (@,1) sin (@,) mw,“ 1- k y = Bd8 = 8, sin d Submit Previous Answers Request Answer X Incorrect; Try Again; 5 attempts remaining

Q1: The system shown has two masses. Beam of mass (Jo#m L² kg.m²) rotates about fixed point (O) and its free end is connected to disk rotates about fixed point (O₂). Consider all connecting links are massless and rigid. Find 1- The displacements of points A, B, and C in addition to the rotations of masses, all in terms of 0. 2- Find the equation of motion (EOM) in terms of 0. 3- What is the natural frequency of the system? 0 L/2 8 Energy methods A Jo=m L²2 L/2 Joz-m R² R C B C 128