A dynamic system in continuous time is specified as in, dx(t) / dt =-2x(t) + 4 and dy(t) / dt = 3x(t) - y(t). Solve for the steady-state values of x(t) and y(t).
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A dynamic system in continuous time is specified as in,
dx(t) / dt =-2x(t) + 4 and dy(t) / dt = 3x(t) - y(t).
Solve for the steady-state values of x(t) and y(t).
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- An ant crawls on the surface of a ball of radius b in such a manner that the ant's motion is given in spherical coordinates by the equations r = b; phi = omega*t; theta = pi/2 * [1 + 1/4 * cos(400t)] Find the speed of the ant as a function of the time t. What sort of path is represented? by the above equations ?Note: Because the argument of the trigonometric functions in this problem will be unitless, your calculator must be in radian mode if you use it to evaluate any trigonometric functions. You will likely need to switch your calculator back into degree mode after this problem.A massless spring is hanging vertically. With no load on the spring, it has a length of 0.24 m. When a mass of 0.59 kg is hung on it, the equilibrium length is 0.98 m. At t=0, the mass (which is at the equilibrium point) is given a velocity of 4.84 m/s downward. At t=0.32s, what is the acceleration of the mass? (Positive for upward acceleration, negative for downward)Using spherical polar coordinates r, 0, p to find CM of a uniform solid hemisphere of radius R, whose flat face lies in the xy plane with its center at the origin. The element of volume is in spherical polars of dV = r² dr sine de dip.
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