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 PRACTICE ITUse the worked example above to help you solve this problem.(a) Find the amplitude, frequency, and period of motion for an object vibrating at the end of ahorizontal spring if the equation for its position as a function of time is the following.A =f =T =amax(b) Find the maximum magnitude of the velocity and acceleration.Vmaxx =V ==a =x = (0.245 m) cos(t)8.00=mHzS(c) What are the position, velocity, and acceleration of the object after 1.50 s has elapsed?mm/sm/s²m/sm/s²

Name: EXAMPLE 13.6 The Vibrating Object-Spring SystemGOAL Identify the phys
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Description: 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 ho

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PRACTICE IT Use the worked example above to help you solve this problem. (a) Find the amplitude, frequency, and period of motion for an object vibrating at the end of a horizontal spring if the equation for its position as a function of time is the following. x (0.245 m) cos(. A = T = m V Hz S a= (b) Find the maximum magnitude of the velocity and acceleration. Vmax= amax = m/s m/s² π 8.00 5t) (c) What are the position, velocity, and acceleration of the object after 1.50 s has elapsed? x = m m/s m/s²