Physics for Scientists and Engineers, Books a la Carte Edition
4th Edition
ISBN: 9780321666680
Author: GIANCOLI, Douglas C.
Publisher: Pearson College Div
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Textbook Question
Chapter 14, Problem 69P
(III) Consider a simple pendulum (point mass bob) 0.50m long with a Q of 350. (a) How long does it take for the amplitude (assumed small) to decrease by two-thirds? (b) If the amplitude is 2.0cm and the bob has mass 0.27 kg, what is the initial energy loss rate of the pendulum in watts? (c) If we are to stimulate resonance with a sinusoidal driving force, how close must the driving frequency he to the natural frequency of the pendulum (give Δf = f − f0)?
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Chapter 14 Solutions
Physics for Scientists and Engineers, Books a la Carte Edition
Ch. 14.1 - An object is oscillating back and forth. Which of...Ch. 14.1 - A mass is oscillating on a frictionless surface at...Ch. 14.1 - If an oscillating mass has a frequency of 1.25 Hz,...Ch. 14.2 - Which of the following represents a simple...Ch. 14.2 - By how much should the mass on the end of a spring...Ch. 14.2 - The position of a SHO is given by x = (0.80 m)...Ch. 14.3 - Suppose the spring in Fig. 1410 is compressed to x...Ch. 14.5 - If a simple pendulum is taken from sea level to...Ch. 14.5 - Return to the Chapter-Opening Question, p. 369,...Ch. 14.5 - (a) Estimate the length of a simple pendulum that...
Ch. 14 - Give some examples of everyday vibrating objects....Ch. 14 - Is the acceleration of a simple harmonic...Ch. 14 - Explain why the motion of a piston in an...Ch. 14 - Real springs have mass. Will the true period and...Ch. 14 - How could you double the maximum speed of a simple...Ch. 14 - A 5.0-kg trout is attached to the hook of a...Ch. 14 - If a pendulum clock is accurate at sea level, will...Ch. 14 - A tire swing hanging from a branch reaches nearly...Ch. 14 - For a simple harmonic oscillator, when (if ever)...Ch. 14 - A 100-g mass hangs from a long cord forming a...Ch. 14 - Two equal masses are attached to separate...Ch. 14 - Does a car bounce on its springs faster when it is...Ch. 14 - What is the approximate period of your walking...Ch. 14 - What happens to the period of a playground swing...Ch. 14 - A thin uniform rod of mass m is suspended from one...Ch. 14 - A tuning fork of natural frequency 264 Hz sits on...Ch. 14 - Why can you make water slosh back and forth in a...Ch. 14 - Give several everyday examples of resonance.Ch. 14 - Is a rattle in a car ever a resonance phenomenon?...Ch. 14 - Over the years, buildings have been able to be...Ch. 14 - (I) If a particle undergoes SHM with amplitude...Ch. 14 - (I) An elastic cord is 65 cm long when a weight of...Ch. 14 - (I) The springs of a 1500-kg car compress 5.0 mm...Ch. 14 - (I) (a) What is the equation describing the motion...Ch. 14 - (II) Estimate the stiffness of the spring in a...Ch. 14 - (II) A fishermans scale stretches 3.6 cm when a...Ch. 14 - (II) Tall buildings are designed to sway in the...Ch. 14 - (II) Construct a Table, indicating the position x...Ch. 14 - (II) A small fly of mass 0.25 g is caught in a...Ch. 14 - (II) A mass m at the end of a spring oscillates...Ch. 14 - (II) A uniform meter stick of mass M is pivoted on...Ch. 14 - (II) A balsa wood block of mass 55g floats on a...Ch. 14 - (II) Figure 1429 shows two examples of SHM,...Ch. 14 - (II) Determine the phase constant in Eq. 144 if,...Ch. 14 - (II) A vertical spring with spring stiffness...Ch. 14 - (II) The graph of displacement vs. time for a...Ch. 14 - (II) The position of a SHO as a function of time...Ch. 14 - (II) A tuning fork oscillates at a frequency of...Ch. 14 - (II) An object of unknown mass m is hung from a...Ch. 14 - (II) A 1.25-kg mass stretches a vertical spring...Ch. 14 - (II) Consider two objects, A and B, both...Ch. 14 - (II) A 1.60-kg object oscillates from a vertically...Ch. 14 - (II) A bungee jumper with mass 65.0 kg jumps from...Ch. 14 - (II) A block of mass m is supported by two...Ch. 14 - (III) A mass m is connected to two springs, with...Ch. 14 - (III) A mass m is at rest on the end of a spring...Ch. 14 - (I) A l.15-kg mass oscillates according to the...Ch. 14 - (I) (a) At what displacement of a SHO is the...Ch. 14 - (II) Draw a graph like Fig. 1411 for a horizontal...Ch. 14 - (II) A 0.35-kg mass at the end of a spring...Ch. 14 - (II) It takes a force of 95.0 to compress the...Ch. 14 - (II) A 0.0125-kg bullet strikes a 0.240-kg block...Ch. 14 - (II) If one oscillation has 5.0 times the energy...Ch. 14 - (II) A mass of 240g oscillates on a horizontal...Ch. 14 - (II) A mass resting on a horizontal, frictionless...Ch. 14 - (II) An object with mass 2.7 kg is executing...Ch. 14 - (II) Agent Arlene devised the following method of...Ch. 14 - (II) Obtain the displacement x as a function of...Ch. 14 - (II) t t = 0, a 785-g mass at rest on the end of a...Ch. 14 - (II) A pinball machine uses a spring launcher that...Ch. 14 - (I) A pendulum has a period of 1.35s on Earth....Ch. 14 - (I) A pendulum makes 32 oscillations in exactly 50...Ch. 14 - (II) A simple pendulum is 0.30m long. At t = 0 it...Ch. 14 - (II) What is the period of a simple pendulum 53cm...Ch. 14 - (II) A simple pendulum oscillates with an...Ch. 14 - (II) Your grandfather clocks pendulum has a length...Ch. 14 - (II) Derive a formula for the maximum speed vmax...Ch. 14 - (II) A pendulum consists of a tiny bob of mass M...Ch. 14 - (II) The balance wheel of a watch is a thin ring...Ch. 14 - (II) The human leg can be compared to a physical...Ch. 14 - (II) (a) Determine the equation of motion (for as...Ch. 14 - (II) A student wants to use a meter stick as a...Ch. 14 - (II) A meter stick is hung at its center from a...Ch. 14 - (II) An aluminum disk. 12.5cm in diameter and 375g...Ch. 14 - (II) A plywood disk of radius 20.0cm and mass...Ch. 14 - (II) A 0.835-kg block oscillates on the end of a...Ch. 14 - (II) Estimate how the damping constant changes...Ch. 14 - (II) A physical pendulum consists of an...Ch. 14 - (II) A damped harmonic oscillator loses 6.0% of...Ch. 14 - (II) A vertical spring of spring constant 115 N/m...Ch. 14 - (III) (a) Show that the total mechanical energy,...Ch. 14 - (III) A glider on an air track is connected by...Ch. 14 - (II) (a) For a forced oscillation at resonance ( =...Ch. 14 - Prob. 64PCh. 14 - (II) An 1150 kg automobile has springs with k =...Ch. 14 - (II) Construct an accurate resonance curve, from ...Ch. 14 - (II) The amplitude of a driven harmonic oscillator...Ch. 14 - (III) By direct substitution, show that Eq. 1422,...Ch. 14 - (III) Consider a simple pendulum (point mass bob)...Ch. 14 - A 62-kg person jumps from a window to a fire net...Ch. 14 - An energy-absorbing car bumper has a spring...Ch. 14 - The length of a simple pendulum is 0.63 m, the...Ch. 14 - A simple pendulum oscillates with frequency f....Ch. 14 - A 0.650-kg mass oscillates according to the...Ch. 14 - (a)A crane has hoisted a 1350-kg car at the...Ch. 14 - An oxygen atom at a particular site within a DNA...Ch. 14 - A seconds pendulum has a period of exactly 2.000...Ch. 14 - A 320-kg wooden raft floats on a lake. When a...Ch. 14 - At what displacement from equilibrium is the speed...Ch. 14 - A diving board oscillates with simple harmonic...Ch. 14 - A rectangular block of wood floats in a calm lake....Ch. 14 - A 950-kg car strikes a huge spring at a speed of...Ch. 14 - A 1.60-kg table is supported on four springs. A...Ch. 14 - In some diatomic molecules, the force each atom...Ch. 14 - A mass attached to the end of a spring is...Ch. 14 - Carbon dioxide is a linear molecule. The...Ch. 14 - Imagine that a 10-cm-diameter circular hole was...Ch. 14 - A thin, Straight, uniform rod of length = 1.00 m...Ch. 14 - A mass m is gently placed on the end of a freely...Ch. 14 - A child of mass m sits on top of a rectangular...Ch. 14 - Estimate the effective spring constant of a...Ch. 14 - In Section 145, the oscillation of a simple...Ch. 14 - (II) A mass m on a frictionless surface is...Ch. 14 - (III) Damping proportional to v2. Suppose the...
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- Give an example of a simple harmonic oscillator, specifically noting how its frequency is independent of amplitude.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_forwardMost harmonic oscillators are damped and, if undriven, eventually come to a stop. Why?arrow_forward
- Check Your Understanding Identify one way you could decrease the maximum velocity of a simple harmonic oscillator.arrow_forwardCan this analogy of SHM to circular motion be carried out with an object oscillating on a spring vertically hung from the ceiling? Why or why not? If given the choice, would you prefer to use a sine function or a cosine function to model the motion?arrow_forwardAn 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_forward
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- Consider a graphical representation (Fig. 12.3) of simple harmonic motion as described mathematically in Equation 12.6. When the particle is at point on the graph, what can you say about its position and velocity? (a) The position and velocity are both positive. (b) The position and velocity are both negative. (c) The position is positive, and the velocity is zero. (d) The position is negative, and the velocity is zero. (e) The position is positive, and the velocity is negative. (f) The position is negative, and the velocity is positive. Figure 12.3 (Quick Quiz 12.2) An xt graph for a particle undergoing simple harmonic motion. At a particular time, the particles position is indicated by in the graph.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_forwardShow that, if a driven oscillator is only lightly damped and driven near resonance, the Q of the system is approximately Q2(TotalenergyEnergylossduringoneperiod)arrow_forward
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