1 Physics And Measurement 2 Motion In One Dimension 3 Vectors 4 Motion In Two Dimensions 5 The Laws Of Motion 6 Circular Motion And Other Applications Of Newton’s Laws 7 Energy Of A System 8 Conservation Of Energy 9 Linear Momentum And Collisions 10 Rotation Of A Rigid Object About A Fixed Axis 11 Angular Momentum 12 Static Equilibrium And Elasticity 13 Universal Gravitation 14 Fluid Mechanics 15 Oscillatory Motion 16 Wave Motion 17 Sound Waves 18 Superposition And Standing Waves 19 Temperature 20 The First Law Of Thermodynamics 21 The Kinetic Theory Of Gases 22 Heat Engines, Entropy, And The Second Law Of Thermodynamics 23 Electric Fields 24 Gauss’s Law 25 Electric Potential 26 Capacitance And Dielectrics 27 Current And Resistance 28 Direct-current Circuits 29 Magnetic Fields 30 Sources Of The Magnetic Field 31 Faraday’s Law 32 Inductance 33 Alternating Current Circuits 34 Electromagnetic Waves 35 The Nature Of Light And The Principles Of Ray Optics 36 Image Formation 37 Wave Optics 38 Diffraction Patterns And Polarization 39 Relativity Chapter15: Oscillatory Motion
Chapter Questions Section: Chapter Questions
Problem 15.1QQ: A block on the end of a spring is pulled to position x = A and released from rest. In one full cycle... Problem 15.2QQ: Consider a graphical representation (Fig. 15.3) of simple harmonic motion as described... Problem 15.3QQ: Figure 15.4 shows two curves representing particles undergoing simple harmonic motion. The correct... Problem 15.4QQ: An object of mass m is hung from a spring and set into oscillation. The period of the oscillation is... Problem 15.5QQ: The ball in Figure 15.13 moves in a circle of radius 0.50 m. At t = 0, the ball is located on the... Problem 15.6QQ: The grandfather clock in the opening storyline depends on the period of a pendulum to keep correct... Problem 15.1OQ: If a simple pendulum oscillates with small amplitude and its length is doubled, what happens to the... Problem 15.2OQ: You attach a block to the bottom end of a spring hanging vertically. You slowly let the block move... Problem 15.3OQ: A block-spring system vibrating on a frictionless, horizontal surface with an amplitude of 6.0 cm... Problem 15.4OQ: An object-spring system moving with simple harmonic motion has an amplitude A. When the kinetic... Problem 15.5OQ: An object of mass 0.40 kg, hanging from a spring with a spring constant of 8.0 N/m, is set into an... Problem 15.6OQ: A runaway railroad car, with mass 3.0 105 kg, coasts across a level track at 2.0 m/s when it... Problem 15.7OQ: The position of an object moving with simple harmonic motion is given by x = 4 cos (6t), where x is... Problem 15.8OQ: If an object of mass m attached to a light spring is replaced by one of mass 9m, the frequency of... Problem 15.9OQ: You stand on the end of a diving board and bounce to set it into oscillation. You find a maximum... Problem 15.10OQ: A mass-spring system moves with simple harmonic motion along the x axis between turning points at x1... Problem 15.11OQ: A block with mass m = 0.1 kg oscillates with amplitude .A = 0.1 in at the end of a spring with force... Problem 15.12OQ: For a simple harmonic oscillator, answer yes or no to the following questions, (a) Can the... Problem 15.13OQ: The top end of a spring is held fixed. A block is hung on the bottom end as in Figure OQ15.13a, and... Problem 15.14OQ: Which of the following statements is not true regarding a mass-spring system that moves with simple... Problem 15.15OQ: A simple pendulum has a period of 2.5 s. (i) What is its period if its length is made four times... Problem 15.16OQ: A simple pendulum is suspended from the ceiling of a stationary elevator, and the period is... Problem 15.17OQ: A particle on a spring moves in simple harmonic motion along the x axis between turning points at x1... Problem 15.1CQ: You are looking at a small, leafy tree. You do not notice any breeze, and most of the leaves on the... Problem 15.2CQ Problem 15.3CQ: If the coordinate of a particle varies as x = -A cos t, what is the phase constant in Equation 15.6?... Problem 15.4CQ: A pendulum bob is made from a sphere filled with water. What would happen to the frequency of... Problem 15.5CQ: Figure CQ15.5 shows graphs of the potential energy of four different systems versus the position of... Problem 15.6CQ: A student thinks that any real vibration must be damped. Is the student correct? If so, give... Problem 15.7CQ: The mechanical energy of an undamped block-spring system is constant as kinetic energy transforms to... Problem 15.8CQ: Is it possible to have damped oscillations when a system is at resonance? Explain. Problem 15.9CQ: Will damped oscillations occur for any values of b and k? Explain. Problem 15.10CQ: If a pendulum clock keeps perfect time al the base of a mountain, will it also keep perfect time... Problem 15.11CQ Problem 15.12CQ: A simple pendulum can be modeled as exhibiting simple harmonic motion when is small. Is the motion... Problem 15.13CQ: Consider the simplified single-piston engine in Figure CQ15.13. Assuming the wheel rotates with... Problem 15.1P: A 0.60-kg block attached to a spring with force constant 130 N/m is free to move on a frictionless,... Problem 15.2P: When a 4.25-kg object is placed on lop of a vertical spring, the spring compresses a distance of... Problem 15.3P: A vertical spring stretches 3.9 cm when a 10-g object is tiling from it. The object is replaced with... Problem 15.4P: In an engine, a piston oscillates with simpler harmonic motion so that its position varies according... Problem 15.5P: The position of a particle is given by the expression x = 4.00 cos {3.00 t + }, where x is in meters... Problem 15.6P: A piston in a gasoline engine is in simple harmonic motion. The engine is running at the rate of 3... Problem 15.7P: A 1.00-kg object is attached to a horizontal spring. The spring is initially stretched by 0.100 m,... Problem 15.8P: A simple harmonic oscillator takes 12.0 s to undergo five complete vibrations. Find (a) the period... Problem 15.9P: A 7.00-kg object is hung from the bottom end of a vertical spring fastened to an overhead beam. The... Problem 15.10P: At an outdoor market, a bunch of bananas attached to the bottom of a vertical spring of force... Problem 15.11P: A vibration sensor, used in testing a washing machine consists of a cube of aluminum 1.50 cm on edge... Problem 15.12P: (a) A hanging spring stretches by 35.0 cm when an object of mass 450 g is hung on it at rest. In... Problem 15.13P: Review. A particle moves along the x axis. It is initially at the position 0.270 m, moving with... Problem 15.14P: A ball dropped from a height of 4.00 m makes an elastic collision with the ground. Assuming no... Problem 15.15P: A particle moving along the x axis in simple harmonic motion starts from its equilibrium position,... Problem 15.16P: The initial position, velocity, and acceleration of an object moving in simple harmonic motion are... Problem 15.17P: A particle moves in simple harmonic motion with a frequency of 3.00 Hz and an amplitude of 5.00 cm.... Problem 15.18P: A 1.00-kg glider attached to a spring with a force constant of 25.0 N/m oscillates on a... Problem 15.19P: A 0.500-kg object attached to a spring with a force constant of 8.00 N/m vibrates in simple harmonic... Problem 15.20P: You attach an object to the bottom end of a hanging vertical spring. It hangs at rest alter... Problem 15.21P: To test the resiliency of its bumper during low-speed collisions, a 1 000-kg automobile is driven... Problem 15.22P: A 200-g block is attached to a horizontal spring and executes simple harmonic motion with a period... Problem 15.23P: A block of unknown mass is attached to a spring with a spring constant of 6.50 N/m and undergoes... Problem 15.24P: A block-spring system oscillates with an amplitude of 3.50 cm. The spring constant is 250 N/m and... Problem 15.25P: A particle executes simple harmonic motion with an amplitude of 3.00 cm. At what position does its... Problem 15.26P: The amplitude of a system moving in simple harmonic motion is doubled. Determine the change in (a)... Problem 15.27P: A 50.0-g object connected to a spring with a force constant of 35.0 N/m oscillates with an amplitude... Problem 15.28P: A 2.00-kg object is attached to a spring and placed on a frictionless, horizontal surface. A... Problem 15.29P: A simple harmonic oscillator of amplitude A has a total energy Determine E, (a) the kinetic energy... Problem 15.30P: Review. A 65.0-kg bungee jumper steps off a bridge with a light bungee cord tied to her body and to... Problem 15.31P: Review. A 0.250-kg block resting on a frictionless, horizontal surface is attached to a spring whose... Problem 15.32P Problem 15.33P: While driving behind a car traveling at 3.00 m/s, you notice that one of the cars tires has a small... Problem 15.34P: A seconds pendulum is one that moves through its equilibrium position once each second. (The period... Problem 15.35P: A simple pendulum makes 120 complete oscillations in 3.00 min at a location where g = 9.80 m/s2.... Problem 15.36P: A particle of mass m slides without friction inside a hemispherical bowl of radius R. Show that if... Problem 15.37P: A physical pendulum in the form of a planar object moves in simple harmonic motion with a frequency... Problem 15.38P: A physical pendulum in the form of a planar object moves in simple harmonic motion with a frequency... Problem 15.39P: The angular position of a pendulum is represented by the equation = 0.032 0 cos t, where is in... Problem 15.40P: Consider the physical pendulum of Figure 15.16. (a) Represent its moment of inertia about an axis... Problem 15.41P Problem 15.42P: A very light rigid rod of length 0.500 m extends straight out from one end of a meterstick. The... Problem 15.43P: Review. A simple pendulum is 5.00 m long. What is the period of small oscillations for this pendulum... Problem 15.44P: A small object is attached to the end of a string to form a simple pendulum. The period of its... Problem 15.45P: A watch balance wheel (Fig. P15.25) has a period of oscillation of 0.250 s. The wheel is constructed... Problem 15.46P: A pendulum with a length of 1.00 m is released from an initial angle of 15.0. After 1 000 s, its... Problem 15.47P: A 10.6-kg object oscillates at the end of a vertical spring that has a spring constant of 2.05 104... Problem 15.48P: Show that the time rate of change of mechanical energy for a damped, undriven oscillator is given by... Problem 15.49P: Show that Equation 15.32 is a solution of Equation 15.31 provided that b2 4 mk. Problem 15.50P: A baby bounces up and down in her crib. Her mass is 12.5 kg, and the crib mattress can be modeled as... Problem 15.51P: As you enter a fine restaurant, you realize that you have accidentally brought a small electronic... Problem 15.52P: A block weighing 40.0 N is suspended from a spring that has a force constant of 200 N/m. The system... Problem 15.53P: A 2.00-kg object attached to a spring moves without friction (b = 0) and is driven by an external... Problem 15.54P: Considering an undamped, forced oscillator (b = 0), show that Equation 15.35 is a solution of... Problem 15.55P: Damping is negligible for a 0.150-kg object hanging from a light, 6.30-N/m spring. A sinusoidal... Problem 15.56AP: The mass of the deuterium molecule (D2) is twice that of the hydrogen molecule (H2). If the... Problem 15.57AP: An object of mass m moves in simple harmonic motion with amplitude 12.0 cm on a light spring. Its... Problem 15.58AP: Review. This problem extends the reasoning of Problem 41 in Chapter 9. Two gliders are set in motion... Problem 15.59AP: A small ball of mass M is attached to the end of a uniform rod of equal mass M and length L that is... Problem 15.60AP: Review. A rock rests on a concrete sidewalk. An earthquake strikes, making the ground move... Problem 15.61AP: Four people, each with a mass of 72.4 kg, are in a car with a mass of 1 130 kg. An earthquake... Problem 15.62AP: To account for the walking speed of a bipedal or quadrupedal animal, model a leg that is not... Problem 15.63AP Problem 15.64AP: An object attached to a spring vibrates with simple harmonic motion as described by Figure P15.33.... Problem 15.65AP: Review. A large block P attached to a light spring executes horizontal, simple harmonic motion as it... Problem 15.66AP: Review. A large block P attached to a light spring executes horizontal, simple harmonic motion as it... Problem 15.67AP: A pendulum of length L and mass M has a spring of force constant k connected to it at a distance h... Problem 15.68AP: A block of mass m is connected to two springs of force constants k1 and k2 in two ways as shown in... Problem 15.69AP: A horizontal plank of mass 5.00 kg and length 2.00 m is pivoted at one end. The planks other end is... Problem 15.70AP: A horizontal plank of mass m and length L is pivoted at one end. The planks other end is supported... Problem 15.71AP: Review. A particle of mass 4.00 kg is attached to a spring with a force constant of 100 N/m. It is... Problem 15.72AP: A ball of mass m is connected to two rubber bands of length L, each under tension T as shown in... Problem 15.73AP: Review. One end of a light spring with force constant k = 100 N/m is attached to a vertical wall. A... Problem 15.74AP: People who ride motorcycles and bicycles learn to look out for bumps in the road and especially for... Problem 15.75AP: A simple pendulum with a length of 2.23 m and a mass of 6.74 kg is given an initial speed of 2.06... Problem 15.76AP: When a block of mass M, connected to the end of a spring of mass ms = 7.40 g and force constant k,... Problem 15.77AP: Review. A light balloon filled with helium of density 0.179 kg/m3 is tied to a light string of... Problem 15.78AP: Consider the damped oscillator illustrated in Figure 15.19. The mass of the object is 375 g, the... Problem 15.79AP: A particle with a mass of 0.500 kg is attached to a horizontal spring with a force constant of 50.0... Problem 15.80AP: Your thumb squeaks on a plate you have just washed. Your sneakers squeak on the gym floor. Car tires... Problem 15.81AP: Review. A lobstermans buoy is a solid wooden cylinder of radius r and mass M. It is weighted at one... Problem 15.82AP Problem 15.83AP: Two identical steel balls, each of mass 67.4 g, are moving in opposite directions at 5.00 m/s. They... Problem 15.84CP: A smaller disk of radius r and mass m is attached rigidly to the face of a second larger disk of... Problem 15.85CP: An object of mass m1 = 9.00 kg is in equilibrium when connected to a light spring of constant k =... Problem 15.86CP: Review. Why is the following situation impassible? You are in the high-speed package delivers... Problem 15.87CP: A block of mass M is connected to a spring of mass m and oscillates in simple harmonic motion on a... Problem 15.88CP: Review. A system consists of a spring with force constant k = 1 250 N/m, length L = 1.50 m, and an... Problem 15.89CP: A light, cubical container of volume a3 is initially filled with a liquid of mass density as shown... Problem 15.2CQ
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Concept explainers
A point rotates about the origin in the ?? plane at a constant radius of 0.266 m with an angular velocity of 8.01 rad/s. The projection of this point's motion on the ?- or ?-axis is simple harmonic.
What is the amplitude of the projected simple harmonic motion ?
What is the projected motion's frequency?
What is the projected motion's period?
Definition Definition Rate of change of angular displacement. Angular velocity indicates how fast an object is rotating. It is a vector quantity and has both magnitude and direction. The magnitude of angular velocity is represented by the length of the vector and the direction of angular velocity is represented by the right-hand thumb rule. It is generally represented by ω.
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