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Rod pendulum A uniform rod of length 2a is suspended from a fixed point O by a light inextensible string of length b attached to one of its ends. The system moves in a vertical plane through O. Take as coordinates the angles θ, Φ between the string and the rod respectively and the downward vertical. Show that the equations governing small oscillations of the system about θ = Φ = 0 are
bθ·· + aΦ·· = -gθ,
bθ·· + (4/3)aΦ·· = -gΦ.
For the special case in which b = 4a/5, find the normal frequencies and the forms of the normal modes. Is the general motion periodic?
In Figure 15.26, the load impedance is 0.2λ from the first stub (stub (1)) and the distance between the two stubs is 0.1 λ. Calculate the lengths of the two stubs to match the load to the line.
1. Each of the following exercises requires evaluating the quality of a two-phase liquid-vapor mixture: (a) The quality of a two-phase liquid-vapor mixture of H2O at 40°C with a specific volume of 10 m3/kg is
What will the velocity and flow of the prototype be? If the measured force on a certain part of the model is 1.5 N, what will the corresponding force on the prototype be?
for the following signals 1024 points were sampled.a 621 hz signal sampled at 850 hzb 1072 hz signal sampled at 1600
Assuming uniform shower flow, estimate the exit velocity from the showerhead jets. loss of the propellant, assuming that the exit gas has a molecular weight of 28.
What staging requirements and site logistics must be discussed and determined during the buyout of the structural steel trade?
At the exit from the first stage nozzles the steam velocity is 244 m/s, specific volume 0.0686 m3 /kg, mean diameter 762 mm and steam angle 76o measured from the axial direction. Determine the nozzle height of this stage.
oxygen enters an insulated 12-cm-diameter pipe with a velocity of 70 ms. at the pipe entrance the oxygen is at 240 kpa
a c-130 pilot desires to fly a low-level navigation mission at 4 n milesmin 240 kn ground speed. winds are forecast out
the upside-down steel a frame shown in the figure is to be bolted to steel beams on the ceiling of a machine room using
For liquid Na, the 1 atm boiling temperature is 1150 K for a flat liquid-vapor interface, ΔHv = 101.3 kJ/mole and γ = 0.19 1/m2. If the liquid pressure is 1 atm, calculate (i) the pressure (in atm) inside a Na bubble with a radius of 1 μm and (ii) ..
an open belt drive connects two pulleys 1.2 and 0.5m diameter on parallel shafts 3.6m apart. the belt has a mass of
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