Water in a U-tube is held at unequal heights by placing a thumb over one end....

  

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Water in a U-tube is held at unequal heights by placing a thumb over one end. The diameter of the tube is 1.5 cm and the total length of the water column is 8 cm, top right to top left. The initial height difference is h as shown in the figure. (a) if we set y=0 at the equilibrium height for the water, what is the value of y, = y(t= 0) for the right column? [3 points] (b) When the thumb is removed, what happens during the next several seconds?| (c) Set up Newton's 2nd law for the water column starting with the pressures. [4 points] (d) Compare the result with the oscillator equation and determine the expression for the angular frequency w. (e) Student I. Maslow Starter began the data collection 0.5[s] after the thumb was removed. The height y at that time was 0.8yo. Determine the velocity of the water column at that time in terms of g, p & yo. (f) Use your values of yo & the initial velocity vo to determine the amplitudes A & B in y = Acos (or)+ B sin (ot) and, from those, find the amplitude D and phase shift & in y = D cos ( ot + 8) (g) The amplitude of the motion decreases by 10% per period. Determine the damping constant Bin e , the damping coefficient, b in F = -bv and the resonance frequency of the damped oscillator. Water in a U-tube is held at unequal heights by placing a thumb over one end. The diameter of the tube is 1.5 cm and the total length of the water column is 8 cm, top right to top left. The initial height difference is h as shown in the figure. (a) if we set y=0 at the equilibrium height for the water, what is the value of y, = y(t= 0) for the right column? [3 points] (b) When the thumb is removed, what happens during the next several seconds?| (c) Set up Newton's 2nd law for the water column starting with the pressures. [4 points] (d) Compare the result with the oscillator equation and determine the expression for the angular frequency w. (e) Student I. Maslow Starter began the data collection 0.5[s] after the thumb was removed. The height y at that time was 0.8yo. Determine the velocity of the water column at that time in terms of g, p & yo. (f) Use your values of yo & the initial velocity vo to determine the amplitudes A & B in y = Acos (or)+ B sin (ot) and, from those, find the amplitude D and phase shift & in y = D cos ( ot + 8) (g) The amplitude of the motion decreases by 10% per period. Determine the damping constant Bin e , the damping coefficient, b in F = -bv and the resonance frequency of the damped oscillator.