A dynamical system is described by the equation where is an order polynomial with roots . In other words, the roots of are the steady states of the system ().
Suppose the system is placed into one of the steady states and is perturbed very slightly away to . How does the perturbation change over time?
Three objects of same heat capacity with temperature , and exchange heat with each other. They are isolated from the rest of the universe. Find the highest possible temperature one of them can reach in kelvin.
Details and assumptions:
Find the Time Period of oscillations (in ) for the arrangement as shown in the figure.
Details and Assumptions:
A dynamical system is described by the equation where is an order polynomial with roots . In other words, the roots of are the steady states of the system ().
Suppose the system is placed into one of the steady states and is perturbed very slightly away to . How does the perturbation change over time?
Toy helicopters with rechargeable batteries fly for a few minutes on a single charge. Manufacturers want to choose the right size of battery to achieve the longest flight time between charges. A larger battery stores more energy, but also increases the mass of the helicopter so it takes more energy to keep it in the air. Our question is, for a helicopter and battery type that behave as specified in the assumptions below, what is the linear size of the battery in mm that will maximize the time the helicopter can hover in place?
Details and assumptions