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)

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.

Q4-6 please

Find the system's natural frequency shown in the figure with references to x. The block moves downward and the disk has radius r and moment inertia (J.) rotates about the fixed point. Assume the cable is rigid with negligible mass. 24 ww Keg 23kme zm

A sketch of a valve and rocker arm system for an internal combustion engine is give in Figure. Model the system as a pendulum attached to a spring and a mass and assume the oil provides viscous damping in the range of 3= 0.01. Determine the equations of motion and calculate an expression for the natural frequency and the damped natural frequency. Here J is the rotational inertia of the rocker arm about its pivot point, k is the stiffness of the valve spring and m is the mass of the valve and stem. Ignore the mass of the spring. Hint: apply Lagrange equation method Rocker arm 0 J k m Solution: Ꮎ Follower k Valve spring Oil Cam m Valve l x

Find the natural frequency (in Hertz) of the system illustrated in the following figure. Assume the disk is rolling without slipping. K1 = 4 MN/m, K2 = 2K1, M = 165 kg, and R = 0.2 m. Assume the moment of inertia is A K, R. K2 www M No Slip 220.19 Hz 35.04 Hz 25.58 Hz 17.94 Hz 71.49 Hz O 0 O O O

Vibrations show all steps and solutions

Find a single equivalent damping constant for the following cases: a) When three dampers are parallel. b) When three dampers are in series. c) When three dampers are connected to a rigid bar in the figure and the equivalent damper is at site c1.

Answer full steps with big clear handwritten please

The figure shows a bar of mass M-4 Kg and length L-1 m, has a concentrated mass at the end of the bar of m= 4 kg. The bar is supported by a pin at O and three springs as shown. In the value k- 800 N/m Find the natural frequency of the system. 2k O 17.0 rad/s O 14.4 rad/s O 10.9 rad/s 20.3 rad/s elle 00000 + 4 1 2 k > bar of mass M mass m