Answer Happy

(a) A general basic vibratory system consists of mass and spring. Figure Q1 shows the vibration knowledge application of multiple parallel springs installed in between the Caterpillar diesel engine generator and the foundation slab (inside the red dash box). Given that the mass of the diesel engine generator is W=Qkg, the spring equivalent stiffness is keq​=RN/m and the generator revolution per minute is RPM=S RPM. Assume that the system is a single degree of freedom and undergoes only vertical translational movement.
(i) Sketch free body diagram of the system together with the action and reaction force magnitude and direction. (2 marks) (ii) Compare the value of spring displacement, x for the free vibration and force vibration of 10kN if the diesel engine generator excites 1 m/s2 during operation. Neglect the gravitational effect. ( 8 marks) (iii) Determine the number of cycles per second for the diesel engine generator. (2 marks) Vibrations of harmonic motion can be represented in a vectorial form. Analyze the values of displacement, velocity, and acceleration if the amplitude, A=2+T m, angular velocity, ω=4+U rad/s and time, t=1 s. The values of T and U depend on the respective 5th  and 6th  digits of your matric number. For example, if your matric number is AD201414, it gives the value of T=1 and U=4.
Figure Q1