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Two mass-spring systems are oscillating with the same total energy, but system A's am- plitude is twice that of system B. How do their spring constants compare?

Two mass-spring systems are oscillating with the same total energy, but system A's am- plitude is twice that of system B. How do their spring constants compare?

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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I want number 60 answers only. 

in the Show that the period of the oscillations is 27 V2R/g. (Hint: You may find the paral- lel-axis theorem useful.) mass FIGURE 13.31 Problem 58 59. A mass m is mounted between two springs with constants k and k, as shown in Fig. 13.32. Show that the angu- k1 k2 www lar frequency of oscillation V(k + k2)/m. iS W = FIGURE 13.32 Problem 59 60. Two mass-spring systems are oscillating with the same total energy, but system A's am- plitude is twice that of system B. How do their spring constants compare? 61. Show that the potential y of a simple pendulum is propor- tional to the square of ngular displacement in the small- amplitude limit. 62. The total energy of a mass-spring system is the sum of its kinetic 1 %3D 2. CH and potential energy: E = mv? + constant, differentiate both sides of this expression with respect to mv² kx². Assuming E remains 2. tin
Transcribed Image Text:in the Show that the period of the oscillations is 27 V2R/g. (Hint: You may find the paral- lel-axis theorem useful.) mass FIGURE 13.31 Problem 58 59. A mass m is mounted between two springs with constants k and k, as shown in Fig. 13.32. Show that the angu- k1 k2 www lar frequency of oscillation V(k + k2)/m. iS W = FIGURE 13.32 Problem 59 60. Two mass-spring systems are oscillating with the same total energy, but system A's am- plitude is twice that of system B. How do their spring constants compare? 61. Show that the potential y of a simple pendulum is propor- tional to the square of ngular displacement in the small- amplitude limit. 62. The total energy of a mass-spring system is the sum of its kinetic 1 %3D 2. CH and potential energy: E = mv? + constant, differentiate both sides of this expression with respect to mv² kx². Assuming E remains 2. tin
Show that the period of the oscillations is 27 V2R/g. (Hint: You may find the paral- lel-axis theorem useful.) e FIGURE 13.31 Problem 58 59. A mass m is mounted between two springs with constants k, and k, as shown in Fig. 13.32. Show that the angu- k1 k2 MWW mww lar frequency of oscillation is w = V(k, + k2)/m. FIGURE 13.32 Problem 59 60. Two mass-spring systems are oscillating with the same total energy, but system A's am- plitude is twice that of system B. How do their spring constants compare? 61. Show that the potential ensv of a simple pendulum is propor- tional to the square of the angular displacement in the small- amplitude limit. 62. The total energy of a mass-spring system is the sum of its kinetic CH and potential energy: E = mv² + 62. 1 2. kx². Assuming E remains constant, differentiate both sides of this expression with respect to
Transcribed Image Text:Show that the period of the oscillations is 27 V2R/g. (Hint: You may find the paral- lel-axis theorem useful.) e FIGURE 13.31 Problem 58 59. A mass m is mounted between two springs with constants k, and k, as shown in Fig. 13.32. Show that the angu- k1 k2 MWW mww lar frequency of oscillation is w = V(k, + k2)/m. FIGURE 13.32 Problem 59 60. Two mass-spring systems are oscillating with the same total energy, but system A's am- plitude is twice that of system B. How do their spring constants compare? 61. Show that the potential ensv of a simple pendulum is propor- tional to the square of the angular displacement in the small- amplitude limit. 62. The total energy of a mass-spring system is the sum of its kinetic CH and potential energy: E = mv² + 62. 1 2. kx². Assuming E remains constant, differentiate both sides of this expression with respect to
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