A mass is attached to the end of a spring and set into oscillation on a horizontal frictionless surface by releasing it from a stretched position. The position of the mass at any time is described by x (7.0 cm)cos[2nt/(4.28 s)]. Determine the following. (a) period of the motion How may the period of oscillation be determined from an expression for the position of the oscillating mass at any time? s (b) frequency of the oscillations How is the frequency of oscillation related to the period of the oscillation? Hz (c) first time the mass is at the position x = 0 What fraction of a period does it take for the oscillating mass to go from the position of maximum positive displacement to the equilibrium position? s (d) first time the mass is at the site of maximum compression of the spring What fraction of a period does it take for the oscillating mass to go from the position of maximum positive displacement to the position of maximum negative displace ment? s

A mass is attached to the end of a spring and set into oscillation on a horizontal frictionless surface by releasing it from a stretched position. The position of the mass at any time is described by x (7.0 cm)cos[2nt/(4.28 s)]. Determine the following. (a) period of the motion How may the period of oscillation be determined from an expression for the position of the oscillating mass at any time? s (b) frequency of the oscillations How is the frequency of oscillation related to the period of the oscillation? Hz (c) first time the mass is at the position x = 0 What fraction of a period does it take for the oscillating mass to go from the position of maximum positive displacement to the equilibrium position? s (d) first time the mass is at the site of maximum compression of the spring What fraction of a period does it take for the oscillating mass to go from the position of maximum positive displacement to the position of maximum negative displace ment? s

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Description: A mass is attached to the end of a spring and set into oscillation on a horizontal frictionless surface by releasing it from a stretched position. The position of the mass at anytime is described by x = (7.0 cm)cos[2nt/(4.28 s)]. Determine the follo

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

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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Concept explainers

Simple harmonic motion

Simple harmonic motion is a type of periodic motion in which an object undergoes oscillatory motion. The restoring force exerted by the object exhibiting SHM is proportional to the displacement from the equilibrium position. The force is directed towards the mean position. We see many examples of SHM around us, common ones are the motion of a pendulum, spring and vibration of strings in musical instruments, and so on.

Simple Pendulum

A simple pendulum comprises a heavy mass (called bob) attached to one end of the weightless and flexible string.

Oscillation

In Physics, oscillation means a repetitive motion that happens in a variation with respect to time. There is usually a central value, where the object would be at rest. Additionally, there are two or more positions between which the repetitive motion takes place. In mathematics, oscillations can also be described as vibrations. The most common examples of oscillation that is seen in daily lives include the alternating current (AC) or the motion of a moving pendulum.

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A mass is attached to the end of a spring and set into oscillation on a horizontal frictionless surface by releasing it from a stretched position. The position of the mass at any
time is described by x = (7.0 cm)cos[2nt/(4.28 s)]. Determine the following.
(a) period of the motion
How may the period of oscillation be determined from an expression for the position of the oscillating mass at any time? s
(b) frequency of the oscillations
How is the frequency of oscillation related to the period of the oscillation? Hz
(c) first time the mass is at the position x = 0
What fraction of a period does it take for the oscillating mass to go from the position of maximum positive displacement to the equilibrium position? s
(d) first time the mass is at the site of maximum compression of the spring
What fraction of a period does it take for the oscillating mass to go from the position of maximum positive displacement to the position of maximum negative
displacement? s

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