A compact, dense object with a mass of 4.10 kg is attached to a spring and is able to oscillate horizontally with negligible friction. The object is pulled to a distance of 0.200 m from its equilibrium position, held in place with a force of 29.0 N, and then released from rest. It then oscillates in simple harmonic motion. (The object ocillates along the x-axis, where x = 0 is the equilibrium position.) (a) What is the spring constant (in N/m)? 145 N/m (b) What is the frequency of the oscillations (in Hz)? .946 V Hz (c) What is the maximum speed of the object (in m/s)? 1.19 V m/s (d) At what position(s) (in m) on the x-axis does the maximum speed occur? X = + 0 m (e) What is the maximum acceleration of the object? (Enter the magnitude in m/s2.) 7.05 v m/s2 (f) At what position(s) (in m) on the x-axis does the maximum acceleration occur? m (g) What is the total mechanical energy of the oscillating spring-object system (in J)? (h) What is the speed of the object (in m/s) when its position is equal to one-third of the maximum displacement from equilibrium? m/s (i) What is the magnitude of the acceleration of the object (in m/s²) when its position is equal to one-third of the maximum displacement from equilibrium? m/s?
A compact, dense object with a mass of 4.10 kg is attached to a spring and is able to oscillate horizontally with negligible friction. The object is pulled to a distance of 0.200 m from its equilibrium position, held in place with a force of 29.0 N, and then released from rest. It then oscillates in simple harmonic motion. (The object ocillates along the x-axis, where x = 0 is the equilibrium position.) (a) What is the spring constant (in N/m)? 145 N/m (b) What is the frequency of the oscillations (in Hz)? .946 V Hz (c) What is the maximum speed of the object (in m/s)? 1.19 V m/s (d) At what position(s) (in m) on the x-axis does the maximum speed occur? X = + 0 m (e) What is the maximum acceleration of the object? (Enter the magnitude in m/s2.) 7.05 v m/s2 (f) At what position(s) (in m) on the x-axis does the maximum acceleration occur? m (g) What is the total mechanical energy of the oscillating spring-object system (in J)? (h) What is the speed of the object (in m/s) when its position is equal to one-third of the maximum displacement from equilibrium? m/s (i) What is the magnitude of the acceleration of the object (in m/s²) when its position is equal to one-third of the maximum displacement from equilibrium? m/s?
Principles of Physics: A Calculus-Based Text
5th Edition
ISBN:9781133104261
Author:Raymond A. Serway, John W. Jewett
Publisher:Raymond A. Serway, John W. Jewett
Chapter12: Oscillatory Motion
Section: Chapter Questions
Problem 18P
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