Hello I have done A and B. Please help me solving C, D and E. Please also take 3 questions from me as well. But DON'T SOLVE a and b. 3. Rotating Tube(a) In a Cartesian plane, if the position vector of a moving particle is givenby ř = rỉ + yj, then the r and y components of velocity is given by #and # respectively. On the other hand, the polar components, i.e., the rand ö components of velocity is given by and r. Using these, provethat the r component of acceleration isdrdef.dt?(10)(b) A smooth straight thin tube revolves with uniform angular velocity w ina vertical plane about one end which is fixed. A particle inside the tube issliding along the tube with a constant velocity v. At time t = 0, the tubewas horizontal and the particle was at a distance a from the fixed end.Show that the motion of the particle can be described by the differentialequationdr- rw? = -g sin wt(11)dt?[Hint: Use formula (10)|(c) Find the complementary function (CF) and the particular integral (PI)of the differential equation (11).(d) Hence or otherwise, show that the general solution can be written asr(t) = L cosh wt + M sinh wt +sin wt(12)%3D(e) Identify the initial conditions from the description in part (b) and usethem to find L and M. Hence show thatr(t) = a cosh wt + (-sinh wt + sin wt2w(13)

Name: Hello I have done A and B. Please help me solving C, D and E. Please a
Uploaded: 2024-03-20T06:38:44.000Z
Channel: Bartleby
Description: Hello I have done A and B. Please help me solving C, D and E. Please also take 3 questions from me as well. But DON'T SOLVE a and b. 3. Rotating Tube(a) In a Cartesian plane, if the position vector of a moving particle is givenby ř = rỉ + yj, then th