EXERCISEIf the object-spring system is described by x = (0.300 m) cos (1.85t), find the following.(a) the amplitude, the angular frequency, the frequency, and the periodA =m@=f =aT =(b) the maximum magnitudes of the velocity and the accelerationVmaxm/sm/s²(c) the position, velocity, and acceleration when t = 0.250 smaxX =V =a =rad/sHz=SmHINTS: GETTING STARTEDm/sm/s²I I'M STUCK! EXAMPLE 13.6 The Vibrating Object-Spring SystemGOAL Identify the physical parameters of a harmonic oscillator from its mathematical description.PROBLEM (a) Find the amplitude, frequency, and period of motion for an object vibrating at the endof a horizontal spring if the equation for its position as a function of time isx = (0.250 m) cos((b) Find the maximum magnitude of the velocity and acceleration. (c) What are the position,velocity, and acceleration of the object after 1.00 s has elapsed?π8.00.t).STRATEGY In part (a) the amplitude and frequency can be found by comparing the given equation withthe standard form, matching up the numerical values with the corresponding terms in the standard form.In part (b) the maximum speed will occur when the sine function equals 1 or -1, the extreme values ofthe sine function (and similarly for the acceleration and the cosine function). In each case, find themagnitude of the expression in front of the trigonometric function. Part (c) is just a matter of substitutingvalues into the necessary equations.SOLUTION(A) Find the amplitude, frequency, and period.Write the standard form of theequation and underneath it write thegiven equation.Equate the factors in front of thecosine functions to find the amplitude.The angular frequency w is the factorin front of t in Equations (1) and (2).Equate these factors.Divide w by 27 to get the frequency f.The period T is the reciprocal of thefrequency.(1) X = A cos(2лft)(2) x = (0.250 m) cos(t)8.00A = 0.250 mw = 2πf =f =T =W2ππ8.00rad/s = 0.393 rad/s= 0.0625 Hz= 16.0 s

Name: EXERCISEIf the object-spring system is described by x = (0.300 m) cos
Uploaded: 2024-03-20T06:58:04.000Z
Channel: Bartleby
Description: EXERCISEIf the object-spring system is described by x = (0.300 m) cos (1.85t), find the following.(a) the amplitude, the angular frequency, the frequency, and the periodA =m@=f =aT =(b) the maximum magnitudes of the velocity and the accelerationVmax

Answered: Image /qna-images/answer/57924449-03a4-412c-a9d0-883d56e373a0.jpg

Science

Physics

EXERCISE If the object-spring system is described by x = (0.300 m) cos (1.851), find the following. (a) the amplitude, the angular frequency, the frequency, and the period A = m @= T = (b) the maximum magnitudes of the velocity and the acceleration Vmax= m/s y = rad/s Hz a = = amax m/s² (c) the position, velocity, and acceleration when t = 0.250 s x = m S HINTS: GETTING STARTED I'M STUCK! m/s m/s²

EXERCISE If the object-spring system is described by x = (0.300 m) cos (1.851), find the following. (a) the amplitude, the angular frequency, the frequency, and the period A = m @= T = (b) the maximum magnitudes of the velocity and the acceleration Vmax= m/s y = rad/s Hz a = = amax m/s² (c) the position, velocity, and acceleration when t = 0.250 s x = m S HINTS: GETTING STARTED I'M STUCK! m/s m/s²

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 12OQ

See similar textbooks

Similar questions

Find the frequency of a tuning fork that takes 2.50103 s to complete one oscillation.
Give an example of a simple harmonic oscillator, specifically noting how its frequency is independent of amplitude.
A pendulum with a period of 2.00000 s in one location (g=9.80m/s2) is moved to a new location where the period is now 1.99796 s. What is the acceleration due to gravity at its new location?
Check Your Understanding Identify one way you could decrease the maximum velocity of a simple harmonic oscillator.
The temperature of the atmosphere oscillates from a maximum near noontime and a minimum near sunrise. Would you consider the atmosphere to be in stable or unstable equilibrium?
A simple harmonic oscillator has amplitude A and period T. Find the minimum time required for its position to change from x = A to x = A/2 in terms of the period T.
The angular position of a pendulum is represented by the equation = 0.032 0 cos t, where is in radians and = 4.43 rad/s. Determine the period and length of the pendulum.
In an engine, a piston oscillates with simple harmonic motion so that its position varies according to the expression x=5.00cos(2t+6) where x is in centimeters and t is in seconds. At t = 0, find (a) the position of the piston, (b) its velocity, and (c) its acceleration. Find (d) the period and (e) the amplitude of the motion.
Some people modify cars to be much closer to the ground than when manufactured. Should they install stiffer springs? Explain your answer.
If a car has a suspension system with a force constant of 5.00104 N/m , how much energy must the car’s shocks remove to dampen an oscillation starting with a maximum displacement of 0.0750 m?
Refer to the problem of the two coupled oscillators discussed in Section 12.2. Show that the total energy of the system is constant. (Calculate the kinetic energy of each of the particles and the potential energy stored in each of the three springs, and sum the results.) Notice that the kinetic and potential energy terms that have 12 as a coefficient depend on C1 and 2 but not on C2 or 2. Why is such a result to be expected?
Some people think a pendulum with a period of 1.00 s can be driven with “mental energy” or psycho kinetically, because its period is the same as an average heartbeat. True or not, what is the length of such a pendulum?