--%>
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 : Convection Heat Transfer Please Solve

    Please Solve this problem Step by step, and the question is in the images.

    		•
  • 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 : Problem on steam turbine 1) A steam

    1) A steam turbine takes in saturated steam at 300oc and outputs steam at 4 bar. When the efficiency of the turbine is 65%, Evaluate: a.  The final composition (vapor vs. liquid) of outgoing steam.b.  The

    		•
  • 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 : Gasoline in Diesel Engine If the

    If the gasoline is used in the Diesel engine explain whether the Diesel engine will work?

    		•
  • 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 : Efficient design What is meant by ‘

    What is meant by ‘efficient design’? Explain.

    		•
  • 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 : 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 : Problem on pressure rise of a water tank

    The water level in a tank is about 20 m above the ground. A hose is joined to the bottom of the tank, and the nozzle in the end of the hose is pointed to straight up. The tank is at sea level, and the water surface is open to the environment. In the line leading from

    		•