A mass is hanging from the ceiling on a spring and oscillating (forever, and without friction). At its highest point, the mass is 12 cm from the floor, and at its lowest point, the mass is 6 cm from the floor. At t = 0, the mass is at its equilibrium and moving downwards, and a single period takes 0.5 seconds. HINT: Graph your y(t) to check your answers. (a) Find a formula for y(t), the position of the mass from the floor as a function of time. (b) What is the position, velocity, and acceleration of the object at t = 2? (c) In its first period, during what time interval(s) is the speed, |v|, of the mass less than 1 cm/s?
A mass is hanging from the ceiling on a spring and oscillating (forever, and without friction). At its highest point, the mass is 12 cm from the floor, and at its lowest point, the mass is 6 cm from the floor. At t = 0, the mass is at its equilibrium and moving downwards, and a single period takes 0.5 seconds. HINT: Graph your y(t) to check your answers. (a) Find a formula for y(t), the position of the mass from the floor as a function of time. (b) What is the position, velocity, and acceleration of the object at t = 2? (c) In its first period, during what time interval(s) is the speed, |v|, of the mass less than 1 cm/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 14P: In an engine, a piston oscillates with simple harmonic motion so that its position varies according...
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