The unbalance of the rotor of a 180-kg motor is equivalent to a mass of 85 g located 150 mm from the axis of rotation. The pad that is placed between the motor and the foundation is equivalent to a spring with a constant of k = 7.5 kN/m in parallel with a dashpot with constant c. Knowing that the magnitude of the maximum acceleration of the motor is 9 mm/s2 at a speed of 100 rpm, determine the damping factor c/cc.

You have made a physical pendulum by swinging a rod of mass M = 1.08 kg and length L = 1.45 meters around its end. The mass of the rod is distributed uniformly along its length. We will assume that the amplitude of the swing is max = 19.34 degrees. Solid Rod Swings in Simple Harmonic Motion ^ 0=-0, max 0=+0₁ max Determine all the following: The FORMULA for the moment of inertia of your rod, I = The distance from the pivot point to the Center-Of-Mass, d = The angular frequency of the pendulum, w = The amplitude of the motion in radians, max = radians The angular velocity when 0 = 64% of full swing, w(0 = 0.64 0max): NOTE: The first question requires a FORMULA, not a value. rad/sec = meters rad/sec

A compact object with a mass of 5.60 kg oscillates at the end of a vertical spring with a spring constant of 2.00 x 10* N/m. The motion is damped by air resistance, and the damping coefficient is b = 3.00 N. s/m. (a) What is the frequency (in Hz) of the damped oscillation? Hz (b) By what percentage does the amplitude of the oscillation decrease in each cycle? % (c) Over what time interval (in s) does the energy of the system drop to 5.00% of its initial value? (d) What If? The atmosphere of Venus is 50 times thicker than that on Earth. If the effect of air resistance on Venus is represented by b = 150 N s/m, recalculate the answers for parts (a) to (c) for this system if it is set in motion in the atmosphere of Venus. What is the frequency (in Hz) of the damped oscillations? Hz What is the percentage decrease in amplitude in each cycle? % What is the time interval (in s) for the energy to drop to 5.00% of its initial value?

The wheel is attached to the spring. The mass of the wheel is m=20 kg. The radius of the wheel is 0.6m. The radius of gyration KG=0.4 m. The spring's unstretched length is Lo=1.0 m. The stiffness coefficient of the spring is k-2.0 N/m. The wheel is released from rest at the state 1 when the angle between the spring and the vertical direction is 8-30°. The wheel rolls without slipping and passes the position at the state 2 when the angle is 0=0°. The spring's length at the state 2 is L2=4 m. _(kg-m²) (two decimal (9) The mass moment of inertial about the IC center is IIC=_ places) L₂ State 2 State 1