Problem 1Q: Give some examples of everyday vibrating objects. Which exhibit SHM, at least approximately? Problem 2Q: Is the acceleration of a simple harmonic oscillator ever zero? If so, where? Problem 3Q: Explain why the motion of a piston in an automobile engine is approximately simple harmonic. Problem 4Q: Real springs have mass. Will the true period and frequency be larger or smaller than given by the... Problem 5Q: How could you double the maximum speed of a simple harmonic oscillator (SHO)? Problem 6Q: A 5.0-kg trout is attached to the hook of a vertical spring scale, and then is released. Describe... Problem 7Q: If a pendulum clock is accurate at sea level, will it gain or lose time when taken to high attitude?... Problem 8Q: A tire swing hanging from a branch reaches nearly to the ground (Fig. 1427). How could you estimate... Problem 9Q: For a simple harmonic oscillator, when (if ever) are the displacement and velocity vectors in the... Problem 10Q: A 100-g mass hangs from a long cord forming a pendulum. The mass is pulled a short distance to one... Problem 11Q: Two equal masses are attached to separate identical springsnext to one another. One mass is pulled... Problem 12Q: Does a car bounce on its springs faster when it is empty orwhen it is fully loaded? Problem 13Q: What is the approximate period of your walking step? Problem 14Q: What happens to the period of a playground swing if yourise up from sitting to a standing position? Problem 15Q: A thin uniform rod of mass m is suspended from one end and oscillates with a frequency f. If a small... Problem 16Q: A tuning fork of natural frequency 264 Hz sits on a table atthe front of a room. At the back of the... Problem 17Q: Why can you make water slosh back and forth in a pan onlyif you shake the pan at a certain... Problem 18Q: Give several everyday examples of resonance. Problem 19Q: Is a rattle in a car ever a resonance phenomenon? Explain. Problem 20Q: Over the years, buildings have been able to be built out oflighter and lighter materials. How has... Problem 1P: (I) If a particle undergoes SHM with amplitude 0.18m,what is the total distance it travels in one... Problem 2P: (I) An elastic cord is 65 cm long when a weight of 75 Nhangs from it hut is 85 cm long when a weight... Problem 3P: (I) The springs of a 1500-kg car compress 5.0 mm when its68-kg driver gets into the drivers seat. If... Problem 4P: (I) (a) What is the equation describing the motion of a mass on the end of a spring which is... Problem 5P: (II) Estimate the stiffness of the spring in a childs pogo stick if the child has a mass of 35 kg... Problem 6P: (II) A fishermans scale stretches 3.6 cm when a 2.4-kg fish hangs from it. (a) What is the spring... Problem 7P: (II) Tall buildings are designed to sway in the wind. In a 100-km/h wind, for example, the top of... Problem 8P: (II) Construct a Table, indicating the position x the mass in Fig. 142 at times t = 0, 14T, 12T,... Problem 9P: (II) A small fly of mass 0.25 g is caught in a spiders web. The web oscillates predominately with a... Problem 10P: (II) A mass m at the end of a spring oscillates with a frequency of 0.83 Hz. When an additional... Problem 11P: (II) A uniform meter stick of mass M is pivoted on a hinge at one end and held horizontal by a... Problem 12P: (II) A balsa wood block of mass 55g floats on a lake, bobbing up and down at a frequency of 3.0 Hz.... Problem 13P: (II) Figure 1429 shows two examples of SHM, labeled A and B. For each, what is (a) the amplitude,... Problem 14P: (II) Determine the phase constant in Eq. 144 if, at t = 0, the oscillating mass is at (a) x = A,... Problem 15P: (II) A vertical spring with spring stiffness constant 305 N/m oscillates with an amplitude of 28.0... Problem 16P: (II) The graph of displacement vs. time for a small mass m at the end of a spring is shown in Fig.... Problem 17P: (II) The position of a SHO as a function of time is given by x = 3.8 cos(5t/4 + /6) where t is in... Problem 18P: (II) A tuning fork oscillates at a frequency of 441 Hz and the tip of each prong moves 1.5 mm to... Problem 19P: (II) An object of unknown mass m is hung from a vertical spring of unknown spring constant k, and... Problem 20P: (II) A 1.25-kg mass stretches a vertical spring 0.215 m. If the spring is stretched an additional... Problem 21P: (II) Consider two objects, A and B, both undergoing SHM, but with different frequencies, as... Problem 22P: (II) A 1.60-kg object oscillates from a vertically hanginglight spring once every 0.55 s. (a) Write... Problem 23P: (II) A bungee jumper with mass 65.0 kg jumps from a high bridge. After reaching his lowest point, he... Problem 24P: (II) A block of mass m is supported by two identical parallel vertical springs, each with spring... Problem 25P: (III) A mass m is connected to two springs, with spring constants k1 and k2, in two different ways... Problem 26P: (III) A mass m is at rest on the end of a spring of spring constant k. At t = 0 it is given an... Problem 27P: (I) A l.15-kg mass oscillates according to the equation x = 0.650 cos 7.40t where x is in meters and... Problem 28P: (I) (a) At what displacement of a SHO is the energy half kinetic and half potential? (b) What... Problem 29P: (II) Draw a graph like Fig. 1411 for a horizontal spring whose spring constant is 95 N/m and which... Problem 30P: (II) A 0.35-kg mass at the end of a spring oscillates 2.5 times per second with an amplitude of 0.15... Problem 31P: (II) It takes a force of 95.0 to compress the spring of a toy popgun 0.175 m to load a 0.160-kg... Problem 32P: (II) A 0.0125-kg bullet strikes a 0.240-kg block attached to a fixed horizontal spring whose spring... Problem 33P: (II) If one oscillation has 5.0 times the energy of a second one of equal frequency and mass, what... Problem 34P: (II) A mass of 240g oscillates on a horizontal frictionless surface at a frequency of 3.0 Hz and... Problem 35P: (II) A mass resting on a horizontal, frictionless surface is attached to one end of a spring; the... Problem 36P: (II) An object with mass 2.7 kg is executing simple harmonic motion, attached to a spring with... Problem 37P: (II) Agent Arlene devised the following method of measuring the muzzle velocity of a rifle (Fig.... Problem 38P: (II) Obtain the displacement x as a function of time for the simple harmonic oscillator using the... Problem 39P: (II) t t = 0, a 785-g mass at rest on the end of a horizontal spring (k = 184 N/m) is struck by a... Problem 40P: (II) A pinball machine uses a spring launcher that is compressed 6.0 cm to launch a ball up a 15... Problem 41P: (I) A pendulum has a period of 1.35s on Earth. What is its period on Mars, where the acceleration of... Problem 42P: (I) A pendulum makes 32 oscillations in exactly 50 s. What is its (a) period and (b) frequency? Problem 43P: (II) A simple pendulum is 0.30m long. At t = 0 it is released from rest starling at an angle of 13.... Problem 44P: (II) What is the period of a simple pendulum 53cm long (a) on the Earth, and (a) when it is in a... Problem 45P: (II) A simple pendulum oscillates with an amplitude of 10.0. What fraction of the time does it spend... Problem 46P: (II) Your grandfather clocks pendulum has a length of 0.9930 m. If the clock loses 26s per day, bow... Problem 47P: (II) Derive a formula for the maximum speed vmax of a simple pendulum bob in terms of g, the length... Problem 48P: (II) A pendulum consists of a tiny bob of mass M and a uniform cord of mass m and length . (a)... Problem 49P: (II) The balance wheel of a watch is a thin ring of radius 0.95 cm and oscillates with a frequency... Problem 50P: (II) The human leg can be compared to a physical pendulum, with a natural swinging period al which... Problem 51P: (II) (a) Determine the equation of motion (for as a function of time) for a torsion pendulum, Fig.... Problem 52P: (II) A student wants to use a meter stick as a pendulum. She plans to drill a small hole through the... Problem 53P: (II) A meter stick is hung at its center from a thin wire (Fig. 1435a). It is twisted and oscillates... Problem 54P: (II) An aluminum disk. 12.5cm in diameter and 375g in mass, is mounted on a vertical shaft with very... Problem 55P: (II) A plywood disk of radius 20.0cm and mass 2.20kg has a small hole drilled through it, 2.00cm... Problem 56P: (II) A 0.835-kg block oscillates on the end of a spring whose spring constant is k = 41.0 N/m. The... Problem 57P: (II) Estimate how the damping constant changes when a cars shock absorbers get old and the car... Problem 58P: (II) A physical pendulum consists of an 85-cm-long. 240-g-mass, uniform wooden rod hung from a nail... Problem 59P: (II) A damped harmonic oscillator loses 6.0% of its mechanical energy per cycle. (a) By what... Problem 60P: (II) A vertical spring of spring constant 115 N/m supports a mass of 75 g. The mass oscillates in a... Problem 61P: (III) (a) Show that the total mechanical energy, E=12mv2+12kx2, as a function of lime for a lightly... Problem 62P: (III) A glider on an air track is connected by springs to either end of the track (Fig. 1439). Both... Problem 63P: (II) (a) For a forced oscillation at resonance ( = 0), what is the value of the phase angle 0 in Eq.... Problem 64P Problem 65P: (II) An 1150 kg automobile has springs with k = 16,000 N/m. One of the tires is not properly... Problem 66P: (II) Construct an accurate resonance curve, from = 0 to = 20, for Q = 6.0. Problem 67P: (II) The amplitude of a driven harmonic oscillator reaches a value of 23.7 F0/k at a resonant... Problem 68P: (III) By direct substitution, show that Eq. 1422, with Eqs. 1423 and 1424, is a solution of the... Problem 69P: (III) Consider a simple pendulum (point mass bob) 0.50m long with a Q of 350. (a) How long does it... Problem 70GP: A 62-kg person jumps from a window to a fire net 20.0 m below, which stretches the net 1.1 m. Assume... Problem 71GP: An energy-absorbing car bumper has a spring constant of 430 kN/m. Find the maximum compression of... Problem 72GP: The length of a simple pendulum is 0.63 m, the pendulum hob has a mass of 295 g, and it is released... Problem 73GP: A simple pendulum oscillates with frequency f. What is its frequency if the entire pendulum... Problem 74GP: A 0.650-kg mass oscillates according to the equation x = 0.25 sin(5.50t) where x is in meters and t... Problem 75GP: (a)A crane has hoisted a 1350-kg car at the junkyard. The cranes steel cable is 20.0 m long and has... Problem 76GP: An oxygen atom at a particular site within a DNA molecule can be made to execute simple harmonic... Problem 77GP: A seconds pendulum has a period of exactly 2.000 s. That is, each one-way swing takes 1.000 s. What... Problem 78GP: A 320-kg wooden raft floats on a lake. When a 75-kg man stands on the raft, it sinks 3.5 cm deeper... Problem 79GP: At what displacement from equilibrium is the speed of a SHO half the maximum value? Problem 80GP: A diving board oscillates with simple harmonic motion of frequency 2.5 cycles per second. What is... Problem 81GP: A rectangular block of wood floats in a calm lake. Show that, if friction is ignored, when the block... Problem 82GP: A 950-kg car strikes a huge spring at a speed of 25 m/s (Fig. 1441), compressing the spring 5.0 m.... Problem 83GP: A 1.60-kg table is supported on four springs. A 0.80-kg chunk of modeling clay is held above the... Problem 84GP: In some diatomic molecules, the force each atom exerts on the other can be approximated by... Problem 85GP: A mass attached to the end of a spring is stretched a distance x0 from equilibrium and released. At... Problem 86GP: Carbon dioxide is a linear molecule. The carbon-oxygen bonds in this molecule act very much like... Problem 87GP: Imagine that a 10-cm-diameter circular hole was drilled all the way through the center of the Earth... Problem 88GP: A thin, Straight, uniform rod of length = 1.00 m and mass m = 215g hangs from a pivot at one end.... Problem 89GP: A mass m is gently placed on the end of a freely hanging spring. The mass then falls 32.0 cm before... Problem 90GP: A child of mass m sits on top of a rectangular slab of mass M = 35 kg, which in turn rests on the... Problem 91GP: Estimate the effective spring constant of a trampoline. Problem 92GP: In Section 145, the oscillation of a simple pendulum (Fig. 1446) is viewed as linear motion along... Problem 93GP: (II) A mass m on a frictionless surface is attached to a spring with spring constant k as shown in... Problem 94GP: (III) Damping proportional to v2. Suppose the oscillator of Example 145 is damped by a force... format_list_bulleted