two subway cars as shown in Figure 1 have mass m = 2000 kg and are connected by a coupler that can be modeled as a spring of stiffness k = 280,000 N/m. Use Newton’s method to derive the equations of motion, calculate the natural frequencies and determine the associated mode shapes. also, find the time response x1(t) and x2(t) of the subway initial conditions: x(0)= [ 0, 0.2] with zero initial velocity vector.  

A stream containing toluene (T), heptane (H) and benzene (Z) is fed into a distillation column at a rate of 200kmol/hr. The composition of the feed has molar fractions for T of 0.4, H of 0.2, Z of 0.4. The amount of toluene in the bottoms is 60% the amount of toluene in the distillate. The molar fraction of hexane in the bottom stream is 1/21 and the molar fraction of benzene in the distillate is 2/19. Solve for the distillate and bottoms and the molar composition of both outlet streams.

You consider investing in an emerging market. Its stock market volatility (standard deviation of returns measured in U.S. dollars) is 25%. The volatility of the World index of developed markets is 15%. The correlation between the emerging market and the World index is 0.2.

a. What would be the volatility of a portfolio invested 95% in the World index and 5% in this emerging market?

b. Compare the result found in the previous question with the volatility of the World index and give an intuitive explanation.

Consider the following returns. The Correlation between Stock X's and Stock Z's returns is closest to: Year End Stock X Realized Return Stock Y Realized Return Stock Z Realized Return 2004 20.1% -14.6% 0.2% 2005 72.7% 4.3% -3.2% 2006 -25.7% -58.1% -27.0% 2007 56.9% 71.1% 27.9% 2008 6.7% 17.3% -5.1% 2009 17.9% 0.9% -11.3% 0.71 0.60 0.62 0.05

consider the following returns. The Correlation between Stock X's and Stock Z's returns is closest to: Year End Stock X Realized Return Stock Y Realized Return Stock Z Realized Return 2004 20.1% -14.6% 0.2% 2005 72.7% 4.3% -3.2% 2006 -25.7% -58.1% -27.0% 2007 56.9% 71.1% 27.9% 2008 6.7% 17.3% -5.1% 2009 17.9% 0.9% -11.3% 0.71 0.60 0.62 0.05

In the figure, block 1 of mass m1 slides from rest along a frictionless ramp from height h = 3.3 m and then collides with stationary block 2, which has mass m2 = 5m1. After the collision, block 2 slides into a region where the coefficient of kinetic friction μk is 0.2 and comes to a stop in distance d within that region. What is the value of distance d if the collision is (a) elastic and (b) completely inelastic?

1. A five-year bond with a yield of 11% (compounded annually) pays an 8%

   coupon at the end of each year.

   1. (a) What is the bond’s price?

   2. (b) What is the bond’s duration?

   3. (c) Use the duration to calculate the effect on the bond’s price of a 0.2% de-

      crease in its yield.

   4. (d) Recalculate the bond’s price on the basis of a 10.8% per annum yield and

      verify that the result is in agreement with your answer to (c).

The worldwide sales of cars from 1981-1990 are shown in the table below. Given: α = 0.2 and β = 0.15 (Hint: Use XLMiner) Year Units sold in thousands 1981 888 1982 900 1983 1000 1984 1200 1985 1100 1986 1300 1987 1250 1988 1150 1989 1100 1990 1200 Using the double exponential smoothing, find the value of the root mean square error for the given data.

1. Given the following pmf f(x,y), calculate m_x, m_y, s_x, s_y, s_xy, p_xy, and E[2.5x²-10y³-8x³y²+3]

x2 is the same as x^2, and x3 is  x^3,y2 is y^2

Suppose a TCP client needs to send 3 packets to the TCP server. Before sending the first packet, the estimated RTT is 50 ms, and the estimated deviation of the sample RTT is 10 ms. The parameters α= 0.1, and β = 0.2. The measured sample RTT for the three packets are 60ms, 70 ms, and 40 ms, respectively. Please compute the time out value that was set for each packet right after it is being transmitted out.