F Fosin t m k 2 Figure Qla: System is subjected to a periodic force excitation (a) Derive the equation of motion of the...
3.23 The system shown in Figure P3.23 is acted upon by the forcing function shown. The system parameters are m = 15 kg, k = 75 kN/m,fo = 750 N, and o 15.13 Hz. Tasks: For motion about equilibrium, determine the steady-state amplitude and phase: (a) Free vibration tests result in a log dec, 6, of Im 0.523 (b) c=0. (c) Using the damping from part (a), determine ft)-fo cos ot the range of excitation frequencies such that the amplitude...
Consider a single degree of freedom (SDOF) with mass-spring-damper system subjected to harmonic excitation having the following characteristics: Mass, m = 850 kg; stiffness, k = 80 kN/m; damping constant, c = 2000 N.s/m, forcing function amplitude, f0 = 5 N; forcing frequency, ωt = 30 rad/s. (a) Calculate the steady-state response of the system and state whether the system is underdamped, critically damped, or overdamped. (b) What happen to the steady-state response when the damping is increased to 18000 N.s/m? (Hint: Determine...
Question B A machine on a viscoelastic foundation (Figure 31.1), modelled as a spring mass-damper system is acted upon by a force modelled as a harmonic force: F(t) = 0.2 sin(wt) Force is given in N and time in seconds. W Figure 31.1 Nos Given numerical values: m = 10 kg C=5 M k = 1000 = 1) draw the correct Free-Body-Diagram and determine the equation of motion [2 marks) 2) determine the natural frequency and the damping ratio of...
A 100 [kg] reciprocating internal combustion engine is fitted to a thin, massless beam using a vibrations damper. It is known that a machine with a rotating unbalance experiences a frequency squared harmonic excitation. The magnitude of the rotating unbalance is A = m,e = 0.3 [kg. m). 1. Calculate the nondimensional function for the state that has a steady state amplitude of 10 [mm] at a 90 [rad/s] speed. 2- Determine the frequency ratio, natural frequency, and the beams...
Olt) 1422LLA 1. The system at the right is subject to the harmonic + x(t) force f(t) = Fo sin ot as shown, with amplitude 50 N and a forcing frequency due to a motor (not m shown) with speed = 191 rotations per minute (RPM). Mass m can only translate horizontally and the rod is pinned at point O. The parameters are: r = 5 cm, m= 10 kg, Jo = 1 kg m-, kı = 1000 N/m, ka...
Design dala Observalion deck mass m-25,000 k Danong ratio 0.5% Figure 91. Determine the equation of motion ofthe ๒wer teevibraorntheform (15 marks) mitt) + car)+xt)- where xt) is the horizontal displacement of the top of the tower b) Determine the damped natural frequency, fa (in Hz) of the tower (10 marks) ) A radar device, which inckdes a large rotaling eccentic mass, has been (30 marks) nstalled at the top of the tower Unfortunately, it has a trequency of rotation...
A system is described by the following differential equation: Ï + + 4 x = sin(at) The steady-state response can be written: Xss = A sinot + 0) If the phase angle is: JT O = radians 2 What is the excitation frequency, o ? rad 0 = 0 S rad w = 1 S rad 0 = 2 S rad 0 = 4
1 T I т I N F The transfer function of a linear differential equation is defined by the Laplace transform of output (response function) over the Laplace transform of input (driving force) The block diagram of a system is not unique. F In the system with the first order differential equation, the steady-state error due to unite step function is not zero. F In a system with a sinusoidal input, the response at the steady state is sinusoidal at...
5.4 Consider the system with a required steady-state error of 20%, K(s + 2) s(s +3s + 5) and an adjustable PI controller zero location. KL(s) Show that the corresponding closed-loop characteristic equation is given by s+ a Next, rewrite the equation as 1 + KG(s0 where K K K.a is constant, and Gf(s) is a function of s, and ex amine the effect of shifting the zero on the closed-loop poles. (a) Design the system for a dominant second-order...
2(35%) Consider the system shown below. (a) Derive the equation of motion of the mass m. (b) Find the steady-state displacement of the mass m. (c) Find the force transmitted to the support at P. y()-Ycos wt C2 2(35%) Consider the system shown below. (a) Derive the equation of motion of the mass m. (b) Find the steady-state displacement of the mass m. (c) Find the force transmitted to the support at P. y()-Ycos wt C2