Essential University Physics, Volume 1 and Volume 2 - With Access
3rd Edition
ISBN: 9780134645490
Author: Wolfson
Publisher: PEARSON
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Chapter 13, Problem 66P
A harmonic oscillator is underdamped if the damping constant b is less than
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Chapter 13 Solutions
Essential University Physics, Volume 1 and Volume 2 - With Access
Ch. 13.1 - A typical human heart rate is about 65 beats per...Ch. 13.2 - Two identical mass-spring systems are displaced...Ch. 13.3 - What happens to the period of a pendulum if (l)...Ch. 13.4 - Figure 13.18 shows the paths traced in the...Ch. 13.5 - Two different mass-spring systems are oscillating...Ch. 13.6 - The figure shows displacement-versus-time graphs...Ch. 13.7 - The photo shows a wineglass shattering in response...Ch. 13 - Is a vertically bouncing ball an example of...Ch. 13 - The vibration frequencies of molecules are much...Ch. 13 - What happens to the frequency of a simple harmonic...
Ch. 13 - If the spring of a simple harmonic oscillator is...Ch. 13 - How does the frequency of a simple harmonic...Ch. 13 - How would the frequency of a horizontal massspring...Ch. 13 - When in its cycle is the acceleration of an...Ch. 13 - Explain how simple harmonic motion might be used...Ch. 13 - One pendulum consists of a solid rod of mass m and...Ch. 13 - The x- and y-components of motion of a body are...Ch. 13 - Why is critical damping desirable in a cars...Ch. 13 - Explain why the frequency of a damped system is...Ch. 13 - Opera singers have been known to break glasses...Ch. 13 - What will happen to the period of a massspring...Ch. 13 - How can a system have more than one resonant...Ch. 13 - Prob. 16ECh. 13 - A violin string playing the note A oscillates at...Ch. 13 - The vibration frequency of a hydrogen chloride...Ch. 13 - Write expressions for the displacement x(t) in...Ch. 13 - The top of a skyscraper sways back and forth,...Ch. 13 - A hummingbirds wings vibrate at about 45 Hz. Whats...Ch. 13 - A 200-g mass is attached to a spring of constant k...Ch. 13 - An automobile suspension has an effective spring...Ch. 13 - The quartz crystal in a watch executes simple...Ch. 13 - A 342-g mass is attached to a spring and undergoes...Ch. 13 - A particle undergoes simple harmonic motion with...Ch. 13 - A particle undergoes simple harmonic motion with...Ch. 13 - How long should you make a simple pendulum so its...Ch. 13 - At the heart of a grandfather clock is a simple...Ch. 13 - A 622-g basketball with 24.0-cm diameter is...Ch. 13 - A meter stick is suspended from one end and set...Ch. 13 - A wheel rotates at 600 rpm. Viewed from the edge,...Ch. 13 - The x- and y-components of an objects motion are...Ch. 13 - A 450-g mass on a spring is oscillating at 1.2 Hz....Ch. 13 - A torsional oscillator of rotational inertia 1.6...Ch. 13 - Youre riding in a friends 1400-kg car with bad...Ch. 13 - The vibration of a piano string can be described...Ch. 13 - A massspring system has b/m = 0/5, where b is the...Ch. 13 - A cars front suspension has a natural frequency of...Ch. 13 - A simple model for carbon dioxide consists of...Ch. 13 - Two identical massspring systems consist of 430-g...Ch. 13 - The human eye and muscles that hold it can be...Ch. 13 - A mass m slides along a frictionless horizontal...Ch. 13 - Prob. 44PCh. 13 - A physics student, bored by a lecture on simple...Ch. 13 - A pendulum of length L is mounted in a rocket....Ch. 13 - The protein dynein powers the flagella that propel...Ch. 13 - A mass is attached to a vertical spring, which...Ch. 13 - Derive the period of a simple pendulum by...Ch. 13 - A solid disk of radius R is suspended from a...Ch. 13 - A thin steel beam is suspended from a crane and is...Ch. 13 - A cyclist turns her bicycle upside down to repair...Ch. 13 - An object undergoes simple harmonic motion in two...Ch. 13 - The muscles that drive insect wings minimize the...Ch. 13 - A pendulum consists of a 320-g solid ball 15.0 cm...Ch. 13 - If Jane and Tarzan are initially 8.0 m apart in...Ch. 13 - A small mass measuring device (SMMD) used for...Ch. 13 - A thin, uniform hoop of mass M and radius R is...Ch. 13 - A mass m is mounted between two springs with...Ch. 13 - The equation for an ellipse is (x2/a2) + (y2/b2) =...Ch. 13 - Show that the potential energy of a simple...Ch. 13 - The total energy of a massspring system is the sum...Ch. 13 - A solid cylinder of mass M and radius R is mounted...Ch. 13 - A mass m is free to slide on a frictionless track...Ch. 13 - A 250-g mass is mounted on a spring of constant k...Ch. 13 - A harmonic oscillator is underdamped if the...Ch. 13 - A massless spring with k = 74 N/m hangs from the...Ch. 13 - A meter stick is suspended from a frictionless rod...Ch. 13 - A particle of mass m has potential energy given by...Ch. 13 - Two balls with the same unknown mass m are mounted...Ch. 13 - Two mass-spring systems with the same mass are...Ch. 13 - Two mass-spring systems have the same mass and the...Ch. 13 - A 500-g mass is suspended from a thread 45 cm long...Ch. 13 - A 500-g block on a frictionless, horizontal...Ch. 13 - Repeat Problem 64 for a small solid ball of mass M...Ch. 13 - Youre working on the script of a movie whose plot...Ch. 13 - A 1.2-kg block rests on a frictionless surface and...Ch. 13 - A disk of radius R is suspended from a pivot...Ch. 13 - Prob. 79PCh. 13 - Youre a structural engineer working on a design...Ch. 13 - Show that x(t) = a cos t bsin t represents simple...Ch. 13 - Youre working for the summer with an ornithologist...Ch. 13 - While waiting for your plane to take off, you...Ch. 13 - Youre working for a playground equipment company,...Ch. 13 - Youve inherited your great-grandmothers mantle...Ch. 13 - This problem explores the nonlinear pendulum...Ch. 13 - Physicians and physiologists are interested in the...Ch. 13 - Physicians and physiologists are interested in the...Ch. 13 - Physicians and physiologists are interested in the...Ch. 13 - Physicians and physiologists are interested in the...
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- In an engine, a piston oscillates with simple harmonic motion so that its position varies according to the expression x=5.00cos(2t+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. Find (d) the period and (e) the amplitude of the motion.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_forwardIf 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_forward
- Show 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_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_forwardA simple harmonic oscillator has amplitude A and period T. Find the minimum time required for its position to change from x = A to x = A/2 in terms of the period T.arrow_forward
- For a damped, driven oscillator, show that the average kinetic energy is the same at a frequency of a given number of octaves* above the kinetic energy resonance as at a frequency of the same number of octaves below resonance.arrow_forwardThe mechanical energy of an undamped block-spring system is constant as kinetic energy transforms to elastic potential energy and vice versa. For comparison, explain what happens to the energy of a damped oscillator in terms of the mechanical, potential, and kinetic energies.arrow_forwardAn object of mass m on a spring of stiffness k oscillates with an amplitude A about its equilibrium position. Suppose that m = 300 g, k = 10 N/m, and A = 10 cm. (a) Find the total energy. (b) Find the mechanical frequency of vibration of the mass. (c) Calculate the change in amplitude when the system loses one quantum of energy.arrow_forward
- Consider the damped oscillator illustrated in Figure 12.16a. The mass of the object is 375 g, the spring constant is 100 N/m, and b = 0.100 N s/m. (a) Over what time interval does the amplitude drop to half its initial value? (b) What If? Over what time interval does the mechanical energy drop to half its initial value? (c) Show that, in general, the fractional rate at which the amplitude decreases in a damped harmonic oscillator is one-half the fractional rate at which the mechanical energy decreases.arrow_forwardThe total energy of a simple harmonic oscillator with amplitude 3.00 cm is 0.500 J. a. What is the kinetic energy of the system when the position of the oscillator is 0.750 cm? b. What is the potential energy of the system at this position? c. What is the position for which the potential energy of the system is equal to its kinetic energy? d. For a simple harmonic oscillator, what, if any, are the positions for which the kinetic energy of the system exceeds the maximum potential energy of the system? Explain your answer. FIGURE P16.73arrow_forwardGive an example of a simple harmonic oscillator, specifically noting how its frequency is independent of amplitude.arrow_forward
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