Concept explainers
A Two springs, with spring constants k1 and k2, are connected to a block of mass m on a frictionless, horizontal table (Fig. P16.80). The block is extended a distance x from equilibrium and released from rest. Show that the block executes
FIGURE P16.80
Trending nowThis is a popular solution!
Chapter 16 Solutions
Physics for Scientists and Engineers: Foundations and Connections
- A uniform annular ring of mass m and inner and outer radii a and b, respectively, is pivoted around an axis perpendicular to the plane of the ring at point P (Fig. P16.35). Determine its period of oscillation. FIGURE P16.35arrow_forwardA wooden block (m = 0.600 kg) is connected to a spring and undergoes simple harmonic motion with an amplitude of oscillation of 0.075 m. The frequency of the motion is 12.50 Hz. a. What is the spring constant? b. What is the maximum speed of the block? c. What is the speed of the block when it is 0.015 m away from the equilibrium position?arrow_forward(a) If frequency is not constant for some oscillation, can the oscillation be SHM? (b) Can you think of any examples of harmonic motion where the frequency may depend on the amplitude?arrow_forward
- A restaurant manager has decorated his retro diner by hanging (scratched) vinyl LP records from thin wires. The records have a mass of 180 g, a diameter of 12 in., and negligible thickness. The records oscillate as torsion pendulums. a. Records hung from a small hole near their rims have a period of roughly 3.5 s (Fig. P16.41A). What is the torsion spring constant of the wire? b. If a record is hung from its center hole using a wire of the same torsion spring constant (Fig. P16.41B), what is its period of oscillation? FIGURE P16.41arrow_forwardA spherical bob of mass m and radius R is suspended from a fixed point by a rigid rod of negligible mass whose length from the point of support to the center of the bob is L (Fig. P16.75). Find the period of small oscillation. N The frequency of a physical pendulum comprising a nonuniform rod of mass 1.25 kg pivoted at one end is observed to be 0.667 Hz. The center of mass of the rod is 40.0 cm below the pivot point. What is the rotational inertia of the pendulum around its pivot point?arrow_forward(a) If frequency is not constant for some oscillation, can the oscillation be simple harmonic motion? (b) Can you mink of any examples of harmonic motion where the frequency may depend on the amplitude?arrow_forward
- The position of a particle attached to a vertical spring is given by y=(y0cost)j. The y axis points upward, y0 = 14.5 cm. and = 18.85 rad/s. Find the position of the particle at a. t = 0 and b. t = 9.0 s. Give your answers in centimeters.arrow_forwardA point on the edge of a childs pinwheel is in uniform circular motion as the wheel spins counterclockwise with a frequency of 1.53 Hz. The point is at the location x = 30.00 cm and y = 0 when a stopwatch is started to track the motion (Fig. P16.15). a. What is the period of the circular motion? b. What is the velocity of the point at the instant described? c. What is the acceleration of the point at the instant described? FIGURE P16.15 Problems 15 and 16.arrow_forwardA spring of mass ms and spring constant k is attached to an object of mass M and set into simple harmonic motion on a frictionless, horizontal table. All portions of the spring are assumed to oscillate in phase, and the velocity of each segment dx of the spring with mass dm can be assumed to be proportional to the distance x of that segment from point A in Figure P16.25. a. What is the kinetic energy of the system at the instant the object is moving with speed v? b. What is the frequency of oscillation of the system? FIGURE P16.25arrow_forward
- A simple pendulum of length L hangs from the ceiling of an elevator. a. While the elevator is moving up with constant acceleration a, is the period of the pendulum affected? If so, how? b. Now suppose we hang a particle of mass m on a spring of spring constant k and attach it to the ceiling of the same elevator. How does an upward acceleration a affect the period of this simple harmonic oscillator?arrow_forwardC, N A uniform plank of length L and mass M is balanced on a fixed, semicircular bowl of radius R (Fig. P16.19). If the plank is tilted slightly from its equilibrium position and released, will it execute simple harmonic motion? If so, obtain the period of its oscillation.arrow_forwardThe equations listed in Table 2.2 give position as a function of time, velocity as a function of time, and velocity as a function of position for an object moving in a straight line with constant acceleration. The quantity vxi appears in every equation. (a) Do any of these equations apply to an object moving in a straight line with simple harmonic motion? (b) Using a similar format, make a table of equations describing simple harmonic motion. Include equations giving acceleration as a function of time and acceleration as a function of position. State the equations in such a form that they apply equally to a blockspring system, to a pendulum, and to other vibrating systems. (c) What quantity appears in every equation?arrow_forward
- Physics for Scientists and Engineers: Foundations...PhysicsISBN:9781133939146Author:Katz, Debora M.Publisher:Cengage LearningPrinciples of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningCollege PhysicsPhysicsISBN:9781938168000Author:Paul Peter Urone, Roger HinrichsPublisher:OpenStax College
- Classical Dynamics of Particles and SystemsPhysicsISBN:9780534408961Author:Stephen T. Thornton, Jerry B. MarionPublisher:Cengage LearningUniversity Physics Volume 1PhysicsISBN:9781938168277Author:William Moebs, Samuel J. Ling, Jeff SannyPublisher:OpenStax - Rice UniversityCollege PhysicsPhysicsISBN:9781305952300Author:Raymond A. Serway, Chris VuillePublisher:Cengage Learning