--%>
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 : Problem on basic process of Arena

    Are you able to assist with these two assignments in Arena simulation below? You can use the Basic Process instead of Blocks and Elements.An office of state license bureau has two types of arrivals. Individuals interested in purchasing new plates are chara

    		•
  • Q : What is wrap-around Wrap-around : The

    Wrap-around: The main aim of a wrap-a-round is to make a straight line about a pipe to help in cutting the pipe to its appropriate length. It is employed mostly as a straight edge or a template.   

    		•
  • Q : Arena Are you able to assist with these

    Are you able to assist with these two assignments in Arena simulation below? You can use the Basic Process instead of Blocks and Elements. An office of state license bureau has two types of arrivals. Individuals interested in purchasing new plates are characterized to have inter-arrival times dis

    		•
  • Q : Unilateral and Bilateral Tolerance

    Explain difference between the Unilateral and Bilateral Tolerance?

    		•
  • Q : SI Engines Illustrate why several types

    Illustrate why several types of the sound are generated in different bikes, although they run on the SI Engines?

    		•
  • Q : Medium-sized turbine How pressure of

    How pressure of oil is managed when starting or stopping the medium-sized turbine?

    		•
  • Q : Deareator In Thermal Power Plant, Why

    In Thermal Power Plant, Why Deareator is placed at the Height?

    		•
  • 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

    		•
  • Q : Explain steam turbine diaphragm Steam

    Steam turbine diaphragm: Steam turbine includes of phases, number and size of the phases depends on the break horse-power of the turbine. The phase has set of moving and fixed blades. Moving blades are joined to th

    		•
  • Q : Mode Superposition Method Define Mode

    Define Mode Superposition Method in brief?

    		•