Statement for Linked Answer Questions 82 & 83: The equation of a vibrating rod is given by . Here u is the displacement along the rod and is a function of both position x and time t. To find the response of the vibrating rod, we need to solve this equation using boundary conditions and initial conditions.
- The boundary conditions needed for a rod fixed at the root (x = 0) and free at the tip (x = l) are
- u(x = 0) = 0, (x = l) = 0
- u(x = l) = 0, (x = l) = 0
- u(x = 0) = 0, u(x = l) = 0
- (x = 0) = 0, (x = l) = 0
- The natural frequencies ω of the fixed-free rod can then be obtained using
- cos(ωl/c) = 0
- sin(ωl/c) = 0
- cos(ωc/l) = 0
- cos(ω/c) = 0
Statement for Linked Answer Questions 84 & 85: Air enters the compressor of a gas turbine engine with velocity 127 m/s, density 1.2 kg/m3and stagnation pressure 0.9 MPa. Air exits the compressor with velocity 139 m/s and stagnation pressure 3.15 MPa. Assume that the ratio of specific heats is constant and equal to 1.4.
- The compressor pressure ratio is