--%>
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 : Bearing number ti Diameter of inner and

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

    		•
  • Q : Problem related to mass flow rate Water

    Water flows via a control volume as illustrated in the figure below. At Section (1) the diameter is 40 mm and the velocity profile is given by the V(r) = 10 (4 – r2) m/s, here r is the  distance from the centerline. At Section (2) the mass flow r

    		•
  • Q : Difference between mill and mill-drill

    Difference between mill and mill-drill: Nowadays numerous manufactures are combining machines; a mill-drill is one of such. This is a combination of a drill and a mill, a mill eliminates stock from material (genera

    		•
  • 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

    		•
  • Q : Petroleum technology theories for the

    theories for the origin of petroleum, methods for detection of petroleum deposits, fractional distillation

    		•
  • 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 : Efficient design What is meant by ‘

    What is meant by ‘efficient design’? Explain.

    		•
  • Q : ANSYS - Finite Element Analysis Hello,

    Hello, is the following project possible.

    		•
  • Q : Measuring the Temperature in Wet Bulb

    Explain phenomenon to measure the Temperature in Wet Bulb Thermometer?

    		•
  • Q : Problem on work of compression A diesel

    A diesel engine operates devoid of a spark plug by using the high-temperature gas produced throughout the compression stage to ignite the fuel. During a typical compression, pure air that is originally at 21 °C and 0.95 bar is reversibly and adiabatically compress

    		•