--%>
Assignment Help - homework help

Undamped single degree of freedom

(a) The response for an undamped single degree of freedom system under free vibration is given as where ωn is the natural frequency and A and B are unknown that can be determined from the initial conditions. The response  can also be written as where φ is the phase angle.

Prove that C and φ are:

2071_single degree.jpg

where u(0) and ú (0) are the initial displacement and velocity, correspondingly

(b) Plot the solution given  in part (a) for the case k = 1000 N/m and m = 10 kg for two complete periods for all the following sets of initial situations

(i) u(0) = 0,  ú (0) = 1 m/s
(ii) u(0) = 0.01 m, ú (0) = 0
(iii) u(0) = 0.01 m, ú (0) = 1 m/s
 
(c) Make a three-dimensional surface plot of the amplitude C of an undamped oscillator given in part (a) versus u(0) and ú (0) for the range of initial conditions given by -1 ≤ u(0) ≤ 0.1 m and -1 ≤ ú (0) ≤ 1 m/s for a system with natural frequency of 10 rad/s. Based on the plot, determine the initial conditions that give the maximum and minimum amplitudes.

   Related Questions in Mechanical Engineering

  • Q : Conformance to standards in product

    Conformance to standards and specifications: These are standards laid down by national and international authorities. For instance, in Canada there is the Standards Council of Canada (SCC). The United States has many standards bodies including MIL (US

    		•
  • Q : Brazing and Welding Differentiate the

    Differentiate the term Brazing and Welding?

    		•
  • Q : What is Cotter joint Cotter joint :

    Cotter joint: These kinds of joints are employed to connect two rods that are under compressive or tensile stress. The ends of rods are in the way of a socket and shaft which fit altogether and the cotter is driven into a slot which is common to both

    		•
  • Q : Problem on damping coefficient Vertical

    Vertical suspension system of a car can be modeled as single degree of the freedom system. Consider that the car with mass m consists of four shock absorbers with equal stiffness and damping of k and c, corresspondingly: (a) Due to

    		•
  • Q : Problem on turbulent flow The

    The approximate equation for the velocity distribution in a rectangular channel with the turbulent flow is 655_turbulent flow.jpg

    Q : Bearing number ti Diameter of inner and

    Specify how the Bearing number ti Diameter of the inner and outer can be calculated?

    		•
  • Q : Decrease in entropy with termperature

    Explain that Entropy decreases along with the increase in its temperature?

    		•
  • Q : Define Product Design Specification

    Product Design Specification: Once the basic idea for a product has been made, the next step is to create a product design specification, or PDS. This document must be as comprehensive and as detailed as possible as it forms the basis of all the work

    		•
  • Q : Cavitation elimination by Pump How

    How Cavitation is eliminated by the Pump?

    		•
  • Q : Mechanical design for manufacturing A

    A stone quarry in a remote part of the world requires that stone blocks of 3 cubic feet in volume be moved up a 50 ft long ramp which is inclined at 30 degrees. Since the location is remote, the blocks must be moved usng human power. On a continuous basis, human power

    		•