--%>
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 : Difference between projectile motion

    Difference between projectile motion and rocket motion:A projectile has no motor or rocket on it, therefore all of its momentum is provided to it as it is launched. An illustration of a projectile would be pen which you throw across a room.

    		•
  • Q : ANSYS - Finite Element Analysis Hello,

    Hello, is the following project possible.

    		•
  • Q : Benefits of gear drive Benefits of gear

    Benefits of gear drive: In general, gear drive is helpful for power transmission among two shafts, which are close to each other (at most at 1m distance). Additionally, it has maximum efficiency while transmitting power. It is resilient as compare to

    		•
  • Q : Advantages and disadvantages of using

    Explain advantages and disadvantages of using the LPG in Car?

    		•
  • 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 : Mechatronics Define the tem

    Define the tem Mechatronics and what are its elements?

    		•
  • 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 : 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 : Solar Thermal systems Explain the two

    Explain the two Solar thermal DHW and Solar DHW Solar thermal systems n brief?

    		•
  • Q : Define feasibility study Feasibility

    Feasibility study: In order to take wise investments in a market-place experiencing rising stages of risk, companies are turning to feasibility studies to find out if they must propose new products, services or commence a new business endeavor. The ma

    		•