An object attached to a spring vibrates with simple harmonic motion as described by the figure below. A coordinate plane is shown with t (s) on the horizontal axis and x (cm) on the vertical axis. A curve is shown to make one and a half complete oscillations along t. The curve begins at the origin moving with a steep slope. The curve is moving with increasing x and decreasing slope until it is horizontal and at its maximum at (1, 2). From (1, 2) the slope of the curve becomes negative and steadily decreases until it crosses the t-axis at (2, 0) with a steep negative slope. From (2, 0) the curve continues below the t-axis with increasing slope until it is horizontal and at its minimum at (3, −2). From (3, −2) the slope of the curve steadily increases until the curve crosses the t-axis at (4, 0) with a steep slope. From (4, 0) one oscillation is complete and the curve repeats the same pattern, decreasing slope until the maximum at (5, 2) and continuing decreasing slope until crossing the t-axis at (6, 0) with a steep negative slope. (a) For this motion, find the amplitude. cm (b) For this motion, find the period. s (c) For this motion, find the angular frequency. rad/s (d) For this motion, find the maximum speed. cm/s (e) For this motion, find the maximum acceleration. cm/s2 (f) For this motion, find an equation for its position x in terms of a sine function. (Submit a file with a maximum size of 1 MB.)

Classical Dynamics of Particles and Systems

5th Edition

ISBN:9780534408961

Author:Stephen T. Thornton, Jerry B. Marion

Publisher:Stephen T. Thornton, Jerry B. Marion

Chapter12: Coupled Oscillations

Section: Chapter Questions

Problem 12.22P

See similar textbooks

Related questions

Question

An object attached to a spring vibrates with simple harmonic motion as described by the figure below.

A coordinate plane is shown with t (s) on the horizontal axis and x (cm) on the vertical axis. A curve is shown to make one and a half complete oscillations along t.

The curve begins at the origin moving with a steep slope. The curve is moving with increasing x and decreasing slope until it is horizontal and at its maximum at (1, 2).
From (1, 2) the slope of the curve becomes negative and steadily decreases until it crosses the t-axis at (2, 0) with a steep negative slope.
From (2, 0) the curve continues below the t-axis with increasing slope until it is horizontal and at its minimum at (3, −2).
From (3, −2) the slope of the curve steadily increases until the curve crosses the t-axis at (4, 0) with a steep slope.
From (4, 0) one oscillation is complete and the curve repeats the same pattern, decreasing slope until the maximum at (5, 2) and continuing decreasing slope until crossing the t-axis at (6, 0) with a steep negative slope.

(a) For this motion, find the amplitude.
cm

(b) For this motion, find the period.
s

(c) For this motion, find the angular frequency.
rad/s

(d) For this motion, find the maximum speed.
cm/s

(e) For this motion, find the maximum acceleration.
cm/s²

(f) For this motion, find an equation for its position x in terms of a sine function. (Submit a file with a maximum size of 1 MB.)

Definition Definition Special type of oscillation where the force of restoration is directly proportional to the displacement of the object from its mean or initial position. If an object is in motion such that the acceleration of the object is directly proportional to its displacement (which helps the moving object return to its resting position) then the object is said to undergo a simple harmonic motion. An object undergoing SHM always moves like a wave.

Expert Solution

Trending now

This is a popular solution!

Step by step

Solved in 5 steps with 10 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.