Problem 2.31: Please complete all of the following
Problem 2.31: Please complete all of the following Problem 2.31: An underdamped mass-spring-dashpot system is subject...
Problem 2.31: Please complete all of the following Problem 2.31: An underdamped mass-spring-dashpot system is subject to a periodic force F(t) of a period T and a saw-tooth form, as shown in Fig. P2.31. Assume ζ 0.1. AF(t) T" 2T 3T Figure P2.31 Periodic loading of saw-tooth shape (a) Obtain the Fourier series expansion for the force. (b) Find the Fourier series expansion of the system's steady-state response. (c) For T/T, = 0.5, where T, is the natural period of...
Problem 2: Consider the following periodic signals x(t), a square wave, and yt), a saw tooth 2T The pulses width of x(t) т, wave. Both have the same amplitude A and the same frequency - equal T. The duty-cycle of x(t) is defined as d- T. -A From tables of Fourier Series ofvarious periodic signals, the following formulas are given for your convenience x(= Ad+2Adnacos at+2Ad sna cos 2at+2Adl sun 3xdcos3at яd 2лd Зяd 24 (sin a 1 sin 2asin3ajain...
a-d please 6 (10) Spring Problems: (a) Find the displacement, y(t), (in arbitrary units) as a function of time for the mass in a mass-spring system described by the differential equatiorn Zy" 10y' + 8y = 100 cos 3t + 4et assuming that the mass is released from rest at the equilibrium position. (This forcing function is not very realistic.) (b) Assume the equation from part (a) describes a mass-spring-dashpot system with a dashpot containing honey. Imagine that the honey...
2. (12 points) Apply the result from part 1 to determine the response of a lowpass filter. a) (4 points) Determine the fundamental frequency and non-zero complex exponential Fourier series coeffi- cients of the periodic signal 2π f(t) =-2-5 sin(2nt) + 10 cos(Grt + "") and sketch the Fourier magnitude spectum D versus w and the Fourier phase spectrum LD versus w (b) (2 points) Use Parseval's theorem for the exponential Fourier series to find the power of the signal...
please complete all parts Problem F.7: These are independent problems (a) (5 points) Solve the following integral. (Hint: Think Fourier series.) (cos(nt) - 2sin(5rt)e-Jr dt XCj) (b) (5 points) Find the Fourier transform io of the following signal: 2(t) = sin(4t)sin(30) (c) (5 points) Solve the integral: sin(2t) 4t dt (d) (5 points) Use Parseval's theorem and your Fourier transform table to compute this integral: Problem F.7: These are independent problems (a) (5 points) Solve the following integral. (Hint: Think...
Problem 1. Consider the following mass, spring, and damper system. Let the force F be the input and the position x be the output. M-1 kg b- 10 N s/m k 20 N/nm F = 1 N when t>=0 PART UNIT FEEDBACK CONTROL SYSTEM 5) Construct a unit feedback control for the mass-spring-damper system 6) Draw the block diagram of the unit feedback control system 7) Find the Transfer Function of the closed-loop (CL) system 8) Find and plot the...