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A mass m is attached to a spring with spring constant k on a frictionless table. We stretch and release it a distance to away from the resting position. (a) Sketch the position, velocity, and acceleration plots (time on x-axis). (b) What is the period if: (i) the mass is doubled, (ii) or the spring constant is quadrupled, and (iii) or we double ro but the mass and spring constant remain unchanged? (c) On one plot, sketch the total energy, kinetic energy, and elastic energy with time on the xr-axis. (d) When the mass is at the position -ro/3, what is the velocity? (e) At what distance will the speed of the mass be half of its maximum speed?

A mass m is attached to a spring with spring constant k on a frictionless table. We stretch and release it a distance to away from the resting position. (a) Sketch the position, velocity, and acceleration plots (time on x-axis). (b) What is the period if: (i) the mass is doubled, (ii) or the spring constant is quadrupled, and (iii) or we double ro but the mass and spring constant remain unchanged? (c) On one plot, sketch the total energy, kinetic energy, and elastic energy with time on the xr-axis. (d) When the mass is at the position -ro/3, what is the velocity? (e) At what distance will the speed of the mass be half of its maximum speed?

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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**Problem 6: Oscillations** A mass \( m \) is attached to a spring with spring constant \( k \) on a frictionless table. We stretch and release it a distance \( x_0 \) away from the resting position. - **(a)** Sketch the position, velocity, and acceleration plots (time on \( x \)-axis). - **(b)** What is the period if: - (i) the mass is doubled, - (ii) the spring constant is quadrupled, - (iii) or we double \( x_0 \) but the mass and spring constant remain unchanged? - **(c)** On one plot, sketch the total energy, kinetic energy, and elastic energy with time on the \( x \)-axis. - **(d)** When the mass is at the position \(-x_0/3\), what is the velocity? - **(e)** At what distance will the speed of the mass be half of its maximum speed?
Transcribed Image Text:**Problem 6: Oscillations** A mass \( m \) is attached to a spring with spring constant \( k \) on a frictionless table. We stretch and release it a distance \( x_0 \) away from the resting position. - **(a)** Sketch the position, velocity, and acceleration plots (time on \( x \)-axis). - **(b)** What is the period if: - (i) the mass is doubled, - (ii) the spring constant is quadrupled, - (iii) or we double \( x_0 \) but the mass and spring constant remain unchanged? - **(c)** On one plot, sketch the total energy, kinetic energy, and elastic energy with time on the \( x \)-axis. - **(d)** When the mass is at the position \(-x_0/3\), what is the velocity? - **(e)** At what distance will the speed of the mass be half of its maximum speed?
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