1- For the system shown in Figure 2 a) Find system response when r(t) = 0 and 2(t) is unit step b) Find system response when r(t) is unit step and n(t) = 0. n(t) r(t) sta S K(s+2) c(t) Figure 2 2- What is the maximum force a 50 mm inner diameter single-acting hydraulic cylinder can generate with a fluid pressure of 10MPa?

give the a) A turbine connected to an electric generator through a gearbox can be modelled as illustrated in Figure 1 = 951 kgm² J2 = 950 kgm² equivalent inertias of the rotary system. The shafts provide a stiffness of k1 = 9.9x10¹Nm/Rad k2 = 4.9x106Nm/Rad spectively. The letters in the parameters represent digits of student numbers: A is the third digit, B is the fifth digit, D is the sixth digit, and F is the seventh digit. i) Draw free-body diagrams ii) Write the equations and put them in matrix form iii) Calculate the dynamic stiffness values iv) Find the natural frequencies and draw mode shapes of the system v) Discuss the effect of coupling stiffness k₁₂ on the natural frequencies k₁₁ 01 k12 O Figure Q2.

3:17 AM ← Jonathan Wickert, Kemper Lewis - An Introduction to Mechanical Engineering-Cengage L... Figure P8.3 Problem P8.3 The disk in a computer hard drive spins at 7200 rpm (Figure P8.3). At the radius of 30 mm, a stream of data is magnetically written on the disk, and the spacing between data bits is 25 µm. Determine the number of bits per second that pass by the read/write head. 30 mm 7200 rpm BA um 4G+ 49%

Parameters Mass 5kg A=2 B=7 C(m)=3 D(m)=4.583

Q.5- Consider the liquid-level control system shown in Figure below. assume that the velocity of the power piston (valve) is proportional to pilot-valve displacement x, dy/dt = K₁ X where K₁ is a positive constant. We also assume that the change in the inflow rate q; is negatively proportional to the change in the valve opening y, Q₁ = -Kv y Assuming the following numerical values for the system, C=2 m², R= 0.5 sec/m², K₁=1 m²/ sec K₁=4 sec-¹ or or a=0.25 m, b= 0.75 m, Obtain the transfer function H(s)/Qd(s). 0.01 n.h ANV L= C(Capacitance) R (Resistance)

Q.5- Consider the liquid-level control system shown in Figure below. assume that the velocity of the power piston (valve) is proportional to pilot-valve displacement x, dy/dt = K₁ x or where K, is a positive constant. We also assume that the change in the inflow rate q, is negatively proportional to the change in the valve opening y, q₁ = -Kvy or Assuming the following numerical values for the system, C=2 m², R= 0.5 sec/m², K, 1 m²/ sec. K₁=4 sec¹ a=0.25 m, b= 0.75 m, Obtain the transfer function H(s)/Qg(s). 3 0.. 1. t CC Re

Pump Figure B2

Q5:- in the fig M= 20 kg, c-7 N.s/m, k=10 N/M, the excitation is 10 sin5t, find natural frequency, excition frequency Excitation force, is the device in the resonse Frequency, Is the device under damping? Find the equation of motion A typical accelerometer Schematic of an accelerometer

Consider the system presented in the following figure K, = 500N / m K, = 2000N / m M = 1Kg %3D X, = 20mm %3D Vo = Omm/s %3D The stiffness of the equivalent spring (in N/m) is equal to Choose... The natural frequency in rad/s is equal to The amplitude of vibration (in m) is Choose... Choose... The phase shift of the vibration is Choose...

Q5:- in the fig M= 20 kg, c=7 N.s/m, k=10 N/M, the excitation is 10 sin5t, find natural frequency, excition frequency Excitation force, is the device in the resonse Frequency, Is the device under damping? Find the equation of motion