For a given law of motion of a particle M find a location of a particle for a time ty (in sec), trajectory, velocuty, t...
According to the given equations of motion of the particle M determine the type of trajectory and for a moment of time t=t_1, find its position on the trajectory, its velocity , total tangential and normal acceleration , and a radius of the trajectory curvature. a) X=-2t^2+3,(cm), Y=-5t(cm) , t_1=0.5(s) b) X=-3/(t+2), Y=3t+6, t_1=2
Please show all work and graph #13 Define an equation of path, position of particle M on path at t = ti (sec), velocity, normal, tangent and full accelerations of the particle M, radius of curvature at t = tį. The defined parameters show on the graph. ti, sec Equations of motion of particle M r=x(t), cm y=y(t), cm - 21² + 3 -5t 4t +4 t +1 2 sin cos 1 t + 4 - 3 -4t 313 +...
Find a fundamental matrix for the system x'(t) = Ax(t) for the given matrix A. A 01 0 0 10 0 0 0 0 0 1 00 - 29 10 et 0 0 el 0 -t 0 et 0 0 et O A. X(t) = 1 0 OB. X(t) = 0 51(5 cos 2t - 2 sin 2t) e5t (5 sin 2t+2 cos 2t) 0 0 2t2 cos 5t - 5 sin 5t) 2 (2 sin 5t + 5 cos...
• Only one submission is necessary for each group. = 1. At time t, particle P has position plt) (1 + 2t, 2 + 5t, 3 – 4t), particle Q has position a(t) (-6+t, -14 + 2t, 2 + 3t), and particle R has position F(t) = (18 – 3t, 10 – 2t, –4 + 4t). (a) Do any of the particles ever collide? Which particles, and when and where do they collide? (b) Do any of the paths of...
3 At a given time, the normalised wave function for a particle in a one-dimensional infinite square well -a < x < a is given by 2 sin2 V inside the well and zero outside. Find the probability that a measurement of energy yields the eigenvalue En. (Hint: use data on page 6.) [6] Useful Data and Formulas = 1.60 x 10-19 C Elementary charge e h/2T=1.05 x 10-34 Js Planck's constant 3.00 x 108 m s-1 Speed of light...
1. Find the speed at the given value of t. r(t) = (7t + 4, 5t + 12, 3t + 3), t = 4 v(4) = Find the speed at the given value of t. r(t) = (sin(3t), cos(8t), cos(7t)), t = ! -() =
Q1) Find the Laplace Transform of the following functions: 1. e +5 2. cos(2t)+7sin(2) 3t)+sin(3) 4. 10+ 5t +12-4 5. (+2)e 6. Gcos(21)-
NOTE: PLEASE DO Q.3 Part d and e Answers are given below: Question 3 (16 marks) Consider the periodic signal T v(t)24 cos(2t ) - 4 sin(5t - 2 The signal v is given as an input to a linear time-invariant continuous-time system with fre- quency response 4 0 lwl 2 2 jw H(w) lwlT 2, 1 2 jw (a) 3 marks] Find the fundamental period To and frequency wo of v (b) [3 marks] Express v in cosine sine...
QUESTION 3 After use Laplace Transform to transform the following initial value problem X" +x=e-t, x(0) = 1,x'(0) = 1, S-2 you should get X(s)= (write fraction as (S-2)/(5-4)(8+6) for -). Then, find (s-4)(8+6) x(t)= L-?{X(s)}= (write 5/6 by 5 -30 6' e^{-3t} by e and sin(2t) or cos(3t) by sin(2t) or cos(3t)).
Find the position vector for a particle with acceleration, initial velocity, and initial position given below. a(t) = (2+, 4 sin(t), cos(5t)) v(0) = (-3, -5,0) 7(0) = (-5,2, - 1) F(t)