--%>
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 : State Concurrent Engineering Concurrent

    Concurrent Engineering has happened primarily as a result of the need to shorten product development times, but improving product quality and reducing product life-cycle costs are important considerations. Some companies have even gone to the extent o

    		•
  • Q : Maintenance in Product design

    Maintenance: How frequently and easily the product is to be maintained must be specified. A photocopier shouldn't require a service call from a technician just to add toner. If the product is to be maintenance free, then costs may be increased due to

    		•
  • Q : Problem related to pressure gauge Water

    Water flowing via the vertical pipe is illustrated below. Compute the required pipe diameter for the smaller pipe,‘d’,  given that the two pressure gauges read similar value.

    Q : Undamped single degree of freedom (a)

    (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 

    		•
  • 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 : Welding rod 7018 State abbreviation of

    State abbreviation of the welding rod 7018?

    		•
  • Q : Arena simulation Are you able to modify

    Are you able to modify the attached [HW4-4-1sawModifiedInstructorTemplate] with the information below for this assignment? Modify the attached exercise by adding agent breaks. The 16 hours are divided into two 8-hour shifts. Agent

    		•
  • Q : Change of power in flow of kinetic

    Air at 20 m/s, 260 K, 75 kPa with 5 kg/s flows into a jet engine and it flows out at 500 m/s, 800 K, 75 kPa. What is the change (power) in flow of kinetic energy?

    		•
  • Q : Size and weight in Product design

    Size and weight: If the product is particularly small the cost may be increased if more precise manufacturing methods are demanded. Weight restriction will as well influence materials to be utilized: this in turn will influence the manufacturing proce

    		•
  • Q : P11 and P12 Pipes Explain difference

    Explain difference between the P11 and P12 Pipes?

    		•