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- Consider a particle with a position function given by s(t)=48t-3t^2. When will the the particle decelerate?Find the position of the particle at time t=4. Is the particle moving toward the origin or away from the origin at time t=4?Sketch a direction field for dy/dx = 2t+y^2 Use the direction field to sketch a solution curve for the initial condition y(0) = −1.
- Find the solution for the damped motion. my'' + cy' + ky = 0 with m = 10, k = 90, y(0) = 0.16, y'(0) = 0, c = 10Consider the undamped forcing problem d^2y/dt^2 + 4y = cos ωt. For what value of ω would resonance happen?30. If E 200 cosh 2x sin 2y a,+ 200 sinh 2x cos 2y a, V/m, find the equation of the di- rection line passing through the point P(1,0,0) and sketch it in the z-0 plane for 0 < x < 5 and 0 < y < /4.
- Find the path of a heat-seeking particle placed at point P on a metal plate whose temperature at (x, y) is T(x, y). T(x, y) = 1600 − 6x2 − 3y2, P(7, 7)Use the direction field to sketch the graphs of the solutions that satisfy the given initial conditions. (a) y(0) = 1(b) y(0) = 2(c) y(0) = –1Suppose that the position of one particle at time t is given by x1 = 5 sin(t), y1 = 2 cos(t), 0 ≤ t ≤ 2? and the position of a second particle is given by x2 = −5 + cos(t), y2 = 1 + sin(t), 0 ≤ t ≤ 2?. 1) find the collision points. (Enter your answers as a comma-separated list of ordered pairs. If an answer does not exist, enter DNE.)