Schaum's Outline of College Physics, Twelfth Edition (Schaum's Outlines)
12th Edition
ISBN: 9781259587399
Author: Eugene Hecht
Publisher: McGraw-Hill Education
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Textbook Question
Chapter 11, Problem 44SP
Show that the natural period of vertical oscillation of a mass hung on a Hookean spring is the same as the period of a simple pendulum whose length is equal to the elongation the mass causes when hung on the spring.
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Schaum's Outline of College Physics, Twelfth Edition (Schaum's Outlines)
Ch. 11 - 18. A small metal sphere weighing 10.0 N is hung...Ch. 11 - 19. How much energy is stored in a spring with an...Ch. 11 - 20. Given that a spring oscillates at a frequency...Ch. 11 - 21. If a reed is oscillating in SHM such that each...Ch. 11 - 22. A stretched wire vibrates in SHM such that...Ch. 11 - 23. A horizontal spring is set up like the one in...Ch. 11 - 24. A horizontal spring is set up like the one in...Ch. 11 - 25. A horizontal spring is set up like the one in...Ch. 11 - 26. For the system shown in Fig. 11-3, write an...Ch. 11 - Prob. 27SP
Ch. 11 - 28. What is the value of the temporal period of a...Ch. 11 - 11.29 [I] Assume a simple pendulum swings...Ch. 11 - 30. A pendulum is timed as it swings back and...Ch. 11 - 11.31 [II] A 300-g mass at the end of a Hookean...Ch. 11 - 32. A coiled Hookean spring is stretched 10 cm...Ch. 11 - 33. A 2.5-kg body undergoes SHM and makes exactly...Ch. 11 - 34. A 300-g object attached to the end of a spring...Ch. 11 - 35. A Hookean spring is stretched 20 cm when a...Ch. 11 - 36. A 300-g body fixed at the end of a spring...Ch. 11 - 37. With a 50-g mass at its end, a spring...Ch. 11 - 11.39 [II] A 500-g object is attached to the end...Ch. 11 - 11.40 [II] A popgun uses a spring for which N/cm....Ch. 11 - 11.41 [II] A cubical block on an air table...Ch. 11 - 42. Find the frequency of vibration on Mars for a...Ch. 11 - 43. A “seconds pendulum” beats seconds; that is,...Ch. 11 - 44. Show that the natural period of vertical...Ch. 11 - 45. A particle that is at the origin of...Ch. 11 - 46. A particle vibrates according to the equation...Ch. 11 - 47. A particle oscillates according to the...
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- Show that angular frequency of a physical pendulum phy=mgrCM/I (Eq. 16.33) equals the angular frequency of a simple pendulum smp=g/, (Eq. 16.29) in the case of a particle at the end of a string of length .arrow_forwardShow that the time rate of change of mechanical energy for a damped, undriven oscillator is given by dE/dt = bv2 and hence is always negative. To do so, differentiate the expression for the mechanical energy of an oscillator, E=12mv2+12kx2, and use Equation 12.28.arrow_forwardIf a car has a suspension system with a force constant of 5.00104 N/m , how much energy must the car’s shocks remove to dampen an oscillation starting with a maximum displacement of 0.0750 m?arrow_forward
- If the amplitude of a damped oscillator decreases to 1/e of its initial value after n periods, show that the frequency of the oscillator must be approximately [1 − (8π2n2)−1] times the frequency of the corresponding undamped oscillator.arrow_forwardIf the speed of the observer is increased by 5.0%, what is the period of the pendulum when measured by this observer?arrow_forwardRefer to the problem of the two coupled oscillators discussed in Section 12.2. Show that the total energy of the system is constant. (Calculate the kinetic energy of each of the particles and the potential energy stored in each of the three springs, and sum the results.) Notice that the kinetic and potential energy terms that have 12 as a coefficient depend on C1 and 2 but not on C2 or 2. Why is such a result to be expected?arrow_forward
- An automobile with a mass of 1000 kg, including passengers, settles 1.0 cm closer to the road for every additional 100 kg of passengers. It is driven with a constant horizontal component of speed 20 km/h over a washboard road with sinusoidal bumps. The amplitude and wavelength of the sine curve are 5.0 cm and 20 cm, respectively. The distance between the front and back wheels is 2.4 m. Find the amplitude of oscillation of the automobile, assuming it moves vertically as an undamped driven harmonic oscillator. Neglect the mass of the wheels and springs and assume that the wheels are always in contact with the road.arrow_forwardCheck Your Understanding An engineer builds two simple pendulums. Both are suspended from small wires secured to the ceiling of a room. Each pendulum hovers 2 cm above the floor. Pendulum 1 has a bob with a mass of 10 kg. Pendulum 2 has a bob with a mass of 100 kg. Describe how the motion of the pendulums will differ if the bobs are both displaced by 12°.arrow_forwardA 50.0-g object connected to a spring with a force constant of 35.0 N/m oscillates with an amplitude of 4.00 cm on a frictionless, horizontal surface. Find (a) the total energy of the system and (b) the speed of the object when its position is 1.00 cm. Find (c) the kinetic energy and (d) the potential energy when its position is 3.00 cm.arrow_forward
- Most harmonic oscillators are damped and, if undriven, eventually come to a stop. Why?arrow_forwardA simple pendulum as shown in Fig. 4.24 oscillates back and forth. Use the letter designations in the figure to identify the pendulums position(s) for the following conditions. (There may be more than one answer. Consider the pendulum to be ideal with no energy losses.) (a) Position(s) of instantaneous rest ___ (b) Position(s) of maximum velocity ___ (c) Position(s) of maximum Ek ___ (d) Position(s) of maximum Ep ___ (e) Position(s) of minimum Ek ___ (f) Position(s) of minimum Ep ___ (g) Position(s) after which Ek increases ___ (h) Position(s) after which Ep increases ___ (i) Position(s) after which Ek decreases ___ (j) Position(s) after which Ep decreases ___ Figure 4.24 The Simple Pendulum and Energyarrow_forwardDetermine the period of oscillation of a simple pendulum of length L suspended from the ceiling of a car that rolls down an inclined plane of angle (Fig. P16.73). Dissipative forces between the car and the plane are negligible.arrow_forward
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