

Question 4 (25% total) Use the Duhamel Integral method to determine expression for the response x(t) of an undamped SDO...
2. (25%) Consider an undamped system subject to a rectangular pulse given by F(t) Fo for 0sts to and Ft) = 0 for t > to (a) Find the displacement response x() for 0ststo and t>to, respectively. (b) Find xmax for 0ststo and t> to, respectively.
2. (25%) Consider an undamped system subject to a rectangular pulse given by F(t) Fo for 0sts to and Ft) = 0 for t > to (a) Find the displacement response x() for 0ststo...
2) Use the Duhamel integral method to derive the expressions for the response of the undamped system subjected to the forcing functions shown in fig A. Set up the expression for x[t) in fig. B Ft 0.sto MA 2+ 0.5 € Fig A
Question Four (a) Determine the response x() for the undamped system subjected to the force F as shown below and given by: ts 0.1s F(t) =-600t +120 0.1 <t s 0.2 s t> 0.2s 600t 0 The mass is initially at rest with x 0 at time 1 0. (b) Find the displacement of the mass at 1 0.25 s. k 75 N/m 0.75 kg F), N 1, S 0.2 0.1
Question Four (a) Determine the response x() for the...
State vIIU F(0) 3) (25 pts.) Find the response of an undamped single degree of freedom systerm to the excitation F(t) shown on the right using the convolution integral. cos 21 to
State vIIU F(0) 3) (25 pts.) Find the response of an undamped single degree of freedom systerm to the excitation F(t) shown on the right using the convolution integral. cos 21 to
3) (30 points) A machine tool with a mass of 30 kg is mounted on an undamped foundation of stiffness 1500 N/m. During operation, it is subject to the machining forces shown in the figure below. Use the principle of superposition and the convolution integral to determine the response of the system to each force. (Fo= 250 N, to=1 sec) (Hint: use table 5.1) F(1) 2F F 10 210
Problem 4. Use the convolution integral to find the response y(t) of the LTI system with impulse response h(t) to input x(t) a) x(I)-2expl_2t)u(t) , h(1)-expl-t)u(t)
Find the convolution integral of the following figure pairs: use
the graph method
y(t) X(t) 0 1 2 3 4
A reciprocating pump weighing W-150 lb, is mounted at a middle of a steel plate of thickness 0.5 in., width of 20 in., and clamped along two edges as shown. During operation of pump, the plate is subjected to a harmonic force Ft)-Fo.t) ibl. 0.5 in. Fio),x(t) 100 in. where the amplitude of harmonic force is F俨50 lh and its angular frequency: 62.832 radls Model the system as a simple spring and mass system in the horizontal plane. The mass...
Problem 4: Evaluation of the convolution integral too y(t) = (f * h)(t) = f(t)h(t – 7)dt is greatly simplified when either the input f(t) or impulse response h(t) is the sum of weighted impulse functions. This fact will be used later in the semester when we study the operation of communication systems using Fourier analysis methods. a) Use the convolution integral to prove that f(t) *8(t – T) = f(t – T) and 8(t – T) *h(t) = h(t...
uestion 2 (25% total a) For a lightly-damped SDOF system, let x, and 1,- be the free vibration displacement amplitudes at the initial (reference) moment and m cycles later, respectively. (15%) In the class we concluded that the damping ratio can be estimated using logarithmic decrement as (LI) 27m Does this method still work if instead of displacement amplitudes, we use velocity amplitudes? That is, can be estimated based on 1+m where v, and Vi+ are the free vibration velocity...