## Write a difference equation for the population at the beginning of the nth day after January 1, 2000 with the immigration rate as the excitation of the system.

At the beginning of the year 2000, the country Freedonia had a population p of 100 million people. The birth rate is 4% per annum and the death rate is 2% per annum, compounded daily. That is, the births and deaths occur every day at a uniform fraction of the current population and the next day the number of births and deaths changes because the population changed the previous day. For example, every day the number of people who die is the fraction  0.02/365  of the total population at the end of the previous day (neglect leap-year effects). Every day 275 immigrants enter Freedonia.

(a) Write a difference equation for the population at the beginning of the nth day after January 1, 2000 with the immigration rate as the excitation of the system.

(b) By finding the zero-excitation and zero-state responses of the system determine the population of Freedonia at the beginning of the year 2050.

### design suitable bearings to support the load for at least 5E8 cycles at 1 200 rpm using deepgroove ball bearings.

The shaft shown in Figure P11-4 was designed in Problem 10-19. For the data in row (a) of Table P11-1, and the corresponding diameter of shaft found in Problem 10-19,….

### Find the minimum film thickness for a long bearing with the following data: 30-mm dia, 130 mm long, 0.0015 clearance ratio, 1 500 rpm, ISO VG 100 oil at 200°F, and supporting a load of 7 kN.

1.       A paper machine processes rolls of paper having a density of 984 kg/m3. The paper roll is 1.50-m OD X 22-cm ID X 3.23-m long and is on a simply supported, 22-cm OD, steel….

### Find the minimum film thickness for a bearing with these data: 30-mm dia, 25 mm long, 0.0015 clearance ratio, 1 500 rpm, ON = 30, ISO VG 220 oil at 200°F.

1.       Problem 7-12 estimated the volume of adhesive wear to expect from a steel shaft of 40 mm dia rotating at 250 rpm for 10 years in a plain bronze….