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73.

73. ll Prove that the expression for x(r) in Equation 15.55 is a solu- tion to the equation of motion for a damped oscillator, Equation 15.54, if and only if the angular frequency w is given by the ex- pression in Equation 15.56. 74. ll A block on a frictionless table is connected as shown in FIGURE P1534 to two springs having spring constants k1 and k2. Show that the block's oscillation frequency is given by f= W\":2 +f22 where fl and f2 are the frequencies at which it would oscillate if attached to spring 1 or spring 2 alone. 4- I? 1;. k2 FIGURE P1534 W 75. II A block on a frictionless table is connected as shown in FIGURE P1535 to two springs having spring constants k. and k2. Find an expression for the block's oscillation frequency f in terms of the frequencies f1 and f2 at which it would oscillate if attached to spring 1 or spring 2 alone. ' } I: k. ,- FIGURE \"5.75 79. III A spring is standing upright on a table with its bottom end fastened to the table. A block is dropped from a height 3.0 cm above the top of the spring. The block sticks to the top end of the spring and then oscillates with an amplitude of 10 cm. What is the oscillation frequency? 81. III FIGURE 0:15.31 shows a 200 g uniform rod pivoted at one end. The other end is attached to a hori- zontal spring. The spring is neither stretched nor compressed when the rod hangs straight down. What is the rod's oscillation period? You can assume that the rod's angle from vertical is always small. FIGURE 0:15.31