Mathieu's equation, defined as, đều gt2 + [w2 + 2e cos(2t)] u = 0, describes the stability of a pendulum with natural frequency w whose pivot point is oscillated in the vertical direction at a frequency of 2 and amplitude of 2€. a) assume a regular perturbation expansion, u= u(t) + eui(t) + and solve for uo, uz if the initial conditions are u(0) = 1 and du (0) = 0. b) what modes are resonant at order ? c) write down the equation for order o(42) and determine what frequencies are resonant at the next order.

Laboratory experiments, observational field studies, and model-building are all examples of different forms of scientific investigations.  in what way do laboratory experiments primarily differ from other forms of scientific investigations?   a.  a laboratory experiment is the only accepted form of investigation within the scientific community.  b.  studies about how things behave in nature or studies involving very large objects are best answered through laboratory experiments.  c.  laboratory experiments involve the identification and control of variables.  d.  data can only be generated through laboratory experiments, not other forms of investigation.

What is the stall speed at sea level of an airplane that weights 10000 lbs., has a wing area of 300ft^2, and a maximum lift coefficient of 1.4? what is the stall speed if flaps that double cl, max are applied?

You hang a book bag on a spring scale and place the bag on a platform scale so that the platform scale reads 23.7n and the spring scale reads 13.8n. what is the magnitude of the force that earth exerts on the bag?