--%>
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 : To designe pump how to design e gear

    how to design e gear pump. show the process.

    		•
  • Q : Define spinning jenny Spinning jenny:

    Spinning jenny: It is a multi-spool spinning wheel. It was invented in the year 1764 by James Hargreaves in Stanhill, close to Blackburn, Lancashire in the north west of England (though Thomas Highs is another candidate recognized as inventor).

    		•
  • Q : Energy in the home-personal energy

    Energy in the home personal energy use and home energy efficiency. Estimate your personal Annual Energy Usage for the following - list all data in kWh (KiloWatt hours):

    		•
  • Q : Bernoulli's equation From Bernoulli's

    From Bernoulli's equation we know that presure head + velocity head at inlet and outlet header is same. If so  what is ' W' then in the equation ?

    		•
  • Q : Centrifugal Pump and Reciprocating Pump

    Out of Centrifugal Pump or the Reciprocating Pump, which pump is more efficient?

    		•
  • 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 : Powder Technology Explain the term

    Explain the term Powder Technology?

    		•
  • Q : Problem on head loss The pump

    The pump illustrated in the figure adds 20 kW of power to the flowing water. The only vital loss is that which takes place across the filter at the inlet of the pump. Find out the head loss for this filter. Note that the gage pressure upstream of the filter is negativ

    		•
  • Q : What is pneumatic system Pneumatic

    Pneumatic system is a system which employs air to power something. For illustration, have you seen the tube systems at the bank drive-up tellers? Air is employed to push the tubes back and forth from the teller to customer.

    Q : Product appearance in Product design

    Product appearance: Strongly influenced by the Industrial Designer, the general style? of the product is significant as this will have an influence on materials and manufacturing procedures to be used. The product should be able to grab the customer's

    		•