Amassless string of length 2l +d is stretched between two fixed points at a tension t. a bead of mass m is attached to the string a distance l from each end of the string (i. e. the two beads are a distance d apart) (a) show that small transverse displacements y1 and y2 of the two beads obey 12 marks] (b) find the normal mode frequencies for this system, and describe physically the corre- 3 marks] sponding motions of the beads.

Steam is generated in a boiler of a cogeneration plant at 10 mpa and 450°c at a steady rate of 5 kg/s. in normal operation, steam expands in a turbine to a pressure of 0.5 mpa and is then routed to the process heater, where it supplies the process heat. steam leaves the process heater as a saturated liquid and is pumped to the boiler pressure. in this mode, no steam passes through a condenser, which operates at 20 kpa. (a) determine the power produced in the turbine and the rate at which process heat is supplied in this mode. (b) determine the power produced in the turbine and the rate of process heat supplied if only 60 percent of the steam is routed to the process heater and the remainder is expanded to the condenser pressure. (3.32 mw; 9.69 mw; 4.25 mw; 5.82 mw)

In a system, when potential energy decreases, then entropy also decreases. true false

Aball has an initial velocity of 3 m/s. if there is no friction, what is the highest it could roll?