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P2(10pts): A mass of 3.0 kg is connected to an ideal spring with spring constant k = and free to move on a frictionless horizontal surface as shown in the figure below. The equation 1.0 N/m, of the ideal (un-damped) oscillator has the form: x(t) = Acos(wt + 0) m a. Using Newton's second law, set up the equation of motion, and prove that the solution above is indeed a valid solution. b. What is the natural frequency and period of oscillation T, w in SI units? c. If at time t = 0 the position and velocity are given by x(0) = 0.20 m and v(0) = 0.10 m/s, find both A and . d. What is the total energy of the system? e. BONUS: Prove that the total mechanical energy of the system is a constant in time.

P2(10pts): A mass of 3.0 kg is connected to an ideal spring with spring constant k = and free to move on a frictionless horizontal surface as shown in the figure below. The equation 1.0 N/m, of the ideal (un-damped) oscillator has the form: x(t) = Acos(wt + 0) m a. Using Newton's second law, set up the equation of motion, and prove that the solution above is indeed a valid solution. b. What is the natural frequency and period of oscillation T, w in SI units? c. If at time t = 0 the position and velocity are given by x(0) = 0.20 m and v(0) = 0.10 m/s, find both A and . d. What is the total energy of the system? e. BONUS: Prove that the total mechanical energy of the system is a constant in time.

Chemistry
Chemistry
10th Edition
ISBN:9781305957404
Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Chapter1: Chemical Foundations
Section: Chapter Questions
Problem 1RQ: Define and explain the differences between the following terms. a. law and theory b. theory and...
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P2(10pts): A mass of 3.0 kg is connected to an ideal spring with spring constant k = and free to move on a frictionless horizontal surface as shown in the figure below. The equation 1.0 N/m, of the ideal (un-damped) oscillator has the form: x(t) = Acos(wt + 0) m a. Using Newton's second law, set up the equation of motion, and prove that the solution above is indeed a valid solution. b. What is the natural frequency and period of oscillation T, w in SI units? c. If at time t = 0 the position and velocity are given by x(0) = 0.20 m and v(0) = 0.10 m/s, find both A and . d. What is the total energy of the system? e. BONUS: Prove that the total mechanical energy of the system is a constant in time.
Transcribed Image Text:P2(10pts): A mass of 3.0 kg is connected to an ideal spring with spring constant k = and free to move on a frictionless horizontal surface as shown in the figure below. The equation 1.0 N/m, of the ideal (un-damped) oscillator has the form: x(t) = Acos(wt + 0) m a. Using Newton's second law, set up the equation of motion, and prove that the solution above is indeed a valid solution. b. What is the natural frequency and period of oscillation T, w in SI units? c. If at time t = 0 the position and velocity are given by x(0) = 0.20 m and v(0) = 0.10 m/s, find both A and . d. What is the total energy of the system? e. BONUS: Prove that the total mechanical energy of the system is a constant in time.
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