A 3.70-kg object is attached to a spring and placed on frictionless, horizontal surface. A horizontal force of 30.0 N is required to hold the object at rest when it is pulled 0.200 m from its equilibrium position (the origin of the x axis). The object is now released from rest from this stretched position, and it subsequently undergoes simple harmonic oscillations. (a) Find the force constant of the spring. 150 N/m (b) Find the frequency of the oscillations. 1.01 Hz (c) Find the maximum speed of the object. 1.27 m/s (d) Where does this maximum speed occur? X = + 0 (e) Find the maximum acceleration of the object. 8.1 m/s2 (f) Where does the maximum acceleration occur? X = + 0.2 (g) Find the total energy of the oscillating system. (h) Find the speed of the object when its position is equal to one-third of the maximum value. m/s (i) Find the magnitude of the acceleration of the object when its position is equal to one-third of the maximum value. m/s2
A 3.70-kg object is attached to a spring and placed on frictionless, horizontal surface. A horizontal force of 30.0 N is required to hold the object at rest when it is pulled 0.200 m from its equilibrium position (the origin of the x axis). The object is now released from rest from this stretched position, and it subsequently undergoes simple harmonic oscillations. (a) Find the force constant of the spring. 150 N/m (b) Find the frequency of the oscillations. 1.01 Hz (c) Find the maximum speed of the object. 1.27 m/s (d) Where does this maximum speed occur? X = + 0 (e) Find the maximum acceleration of the object. 8.1 m/s2 (f) Where does the maximum acceleration occur? X = + 0.2 (g) Find the total energy of the oscillating system. (h) Find the speed of the object when its position is equal to one-third of the maximum value. m/s (i) Find the magnitude of the acceleration of the object when its position is equal to one-third of the maximum value. m/s2
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
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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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Transcribed Image Text:A 3.70-kg object is attached to a spring and placed on a frictionless horizontal surface. A horizontal force of 30.0 N is required to hold the object at rest when it is pulled 0.200 m from its equilibrium position (the origin of the x-axis). The object is released from rest from this stretched position, undergoing simple harmonic oscillations.
(a) **Find the force constant of the spring.**
- Answer: 150 N/m
(b) **Find the frequency of the oscillations.**
- Answer: 1.01 Hz
(c) **Find the maximum speed of the object.**
- Answer: 1.27 m/s
(d) **Where does this maximum speed occur?**
- Answer: x = ± 0 m
(e) **Find the maximum acceleration of the object.**
- Answer: 8.1 m/s²
(f) **Where does the maximum acceleration occur?**
- Answer: x = ± 0.2 m
(g) **Find the total energy of the oscillating system.**
- Answer: (Not provided)
(h) **Find the speed of the object when its position is equal to one-third of the maximum value.**
- Answer: (Not provided)
(i) **Find the magnitude of the acceleration of the object when its position is equal to one-third of the maximum value.**
- Answer: (Not provided)
This task involves understanding the principles of simple harmonic motion, calculating spring constants, frequencies, speeds, accelerations, and energy transformations in an oscillating system. Each solution builds on the fundamental equations of motion for a harmonic oscillator.
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