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**Unformatted text preview: **Chapter 15 Problems 1, 2 , 3 = straightforward, intermediate, challenging Note : Neglect the mass of every spring, except in problems 66 and 68. Section 15.1 Motion of an Object Attached to a Spring Problems 15, 16, 19, 23, 56, and 62 in Chapter 7 can also be assigned with this section. 1. A ball dropped from a height of 4.00 m makes a perfectly elastic collision with the ground. Assuming no mechanical energy is lost due to air resistance, (a) show that the ensuing motion is periodic and (b) determine the period of the motion. (c) Is the motion simple harmonic? Explain. Section 15.2 Mathematical Representation of Simple Harmonic Motion 2. In an engine, a piston oscillates with simple harmonic motion so that its position varies according to the expression x = (5.00 cm) cos(2 t + π /6) where x is in centimeters and t is in seconds. At t = 0, find (a) the position of the piston, (b) its velocity, and (c) its acceleration. (d) Find the period and amplitude of the motion. 3. The position of a particle is given by the expression x = (4.00 m) cos(3.00 π t + π ), where x is in meters and t is in seconds. Determine (a) the frequency and period of the motion, (b) the amplitude of the motion, (c) the phase constant, and (d) the position of the particle at t = 0.250 s. 4. (a) A hanging spring stretches by 35.0 cm when an object of mass 450 g is hung on it at rest. In this situation, we define its position as x = 0. The object is pulled down an additional 18.0 cm and released from rest to oscillate without friction. What is its position x at a time 84.4 s later? (b) What If? A hanging spring stretches by 35.5 cm when an object of mass 440 g is hung on it at rest. We define this new position as x = 0. This object is also pulled down an additional 18.0 cm and released from rest to oscillate without friction. Find its position 84.4 s later. (c) Why are the answers to (a) and (b) different by such a large percentage when the data are so similar? Does this circumstance reveal a fundamental difficulty in calculating the future? (d) Find the distance traveled by the vibrating object in part (a). (e) Find the distance traveled by the object in part (b). 5. A particle moving along the x axis in simple harmonic motion starts from its equilibrium position, the origin, at t = 0 and moves to the right. The amplitude of its motion is 2.00 cm and the frequency is 1.50 Hz. (a) Show that the position of the particle is given by x = (2.00 cm) sin(3.00 π t ) Determine (b) the maximum speed and the ...

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