Please solve the below problems 1- A simple pendulum is found to vibrate at a frequency of 0.5 Hz in a vacuum and 0.45 Hz in a viscous fluid medium. Find the damping constant, assuming the mass of the bob of the pendulum is 1 kg. 2- Assuming that the phase angle is zero, show that the response x(t) of an underdamped single degree- of-freedom system reaches a maximum value when ?????? = √1 − ?2 and a minimum value when ?????? = −√1 − ?2 Also show that the equations of the curves passing through the maximum and minimum values of x(t) are given, respectively, by ? = √1 − ?2??−???? and ? = −√1 − ?2??−???? 3- Figure 1 shows an offset slider-crank mechanism with a crank length r, connecting rod length l, and offset δ If the crank has a mass and mass moment of inertia of mr and Jr respectively, at its center of mass A, the connecting rod has a mass and mass moment of inertia of mc and Jc respectively, at its center of mass C, and the piston has a mass mp determine the equivalent rotational inertia of the system about the center of rotation of the crank, point O Figure

Please solve the below problems 1- A simple pendulum is found to vibrate at a frequency of 0.5 Hz in a vacuum and 0.45 Hz in a viscous fluid medium. Find the damping constant, assuming the mass of the bob of the pendulum is 1 kg. 2- Assuming that the phase angle is zero, show that the response x(t) of an underdamped single degree- of-freedom system reaches a maximum value when ?????? = √1 − ?2 and a minimum value when ?????? = −√1 − ?2 Also show that the equations of the curves passing through the maximum and minimum values of x(t) are given, respectively, by ? = √1 − ?2??−???? and ? = −√1 − ?2??−???? 3- Figure 1 shows an offset slider-crank mechanism with a crank length r, connecting rod length l, and offset δ If the crank has a mass and mass moment of inertia of mr and Jr respectively, at its center of mass A, the connecting rod has a mass and mass moment of inertia of mc and Jc respectively, at its center of mass C, and the piston has a mass mp determine the equivalent rotational inertia of the system about the center of rotation of the crank, point O Figure