Sphere, mass m 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° 4 k₁ m 00000 x(1)

Pls see question in the attached image and solve the question by hand written notes and figure.

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

Q2: Find the E.O.M of the system shown in the fig by using newtons law, and then find the total forced displecment if yo = 0.001m and the time of one period is 0.125 s and w₁ = 45.25 rad / sec body 1.6 m/s +

Piston (M=5kg) is driven when the fly wheel (r=0.1m, J=0.5kgm^2) moves the arm (L=0.2m,m=1kg). The stiffness k=100N/m come Fron compression of gas. What is the natural frequency of the system

Question 1 A sketch of a valve and rocker arm system for an internal combustion engine is give in below figure. Model the system as a pendulum attached to a spring and a mass. Determine the equations of motion and calculate the natural frequency in rad/s. The mass moment of inertia of the rocker arm about its pivot point j=0.46, the stiffness of the valve springspring k=420 , the distance from pivot to spring I= 0.98 m, and the mass of the valve m=3.2 kg. Ignore the mass of the spring and the oil effect. Rocker arm Follower k Valve spring LOil Cam m Valve

find the natural frequency of system assume mass of rod is negligible. In given fig shows k 1=1000 N/m k = 2000 N/m m= 10 kg. Please find the attached image for fig.

Vibrations

Derive the differential equation and find the natural frequency. Neglect friction. (Mech. Vibration)

F(1) Spring m. Ball Dashpot Find the motion of the mass-spring system with the driving force F(t) shown above for the given data. [Hint: Read Forced Oscillations notes.] e-2t, 0 2 y(0) = 1, y'(0) =-1.5.