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Part B The same system is being used as in part a but this time the mass m is being pulled down with a force as can be seen in the figure below. Find the equation of motion for this system where m is the mass, k is the stiffness of the spring, x is the displacement and t is the time. I m Fsin(at) F Also, show that x = Acos (wt) + Bsin(wt) + k-ma² sin (at) where A, B are constants and w = A m Transcribed Image Text: Also, show that X = Acos (wt) + Bsin(wt) + constants and w=k}m Fsin(at) m F k-ma² sin (at) where A, B are Now, let, x=D Sin (xt) ; D- constant Substituting this into the equation of motion, - (1) D Sin (1) + (+) sin (-1) = - (D) x + (1) +xt) - (km) D D+ F-KD = F M - D F = - =>>> D 1 So, K-x²m F sin(at) x = Acas (wt) + Bsm (wt) + ((x = x²)) sin (ext) Comparing this equation with the desired form, A = 0, B = 0, K = F+m Now, x= A cos (W)+ BSin (wt) +- F K-ma² Sin(at) [Prored]

Part B The same system is being used as in part a but this time the mass m is being pulled down with a force as can be seen in the figure below. Find the equation of motion for this system where m is the mass, k is the stiffness of the spring, x is the displacement and t is the time. I m Fsin(at) F Also, show that x = Acos (wt) + Bsin(wt) + k-ma² sin (at) where A, B are constants and w = A m Transcribed Image Text: Also, show that X = Acos (wt) + Bsin(wt) + constants and w=k}m Fsin(at) m F k-ma² sin (at) where A, B are Now, let, x=D Sin (xt) ; D- constant Substituting this into the equation of motion, - (1) D Sin (1) + (+) sin (-1) = - (D) x + (1) +xt) - (km) D D+ F-KD = F M - D F = - =>>> D 1 So, K-x²m F sin(at) x = Acas (wt) + Bsm (wt) + ((x = x²)) sin (ext) Comparing this equation with the desired form, A = 0, B = 0, K = F+m Now, x= A cos (W)+ BSin (wt) +- F K-ma² Sin(at) [Prored]

Glencoe Physics: Principles and Problems, Student Edition
Glencoe Physics: Principles and Problems, Student Edition
1st Edition
ISBN:9780078807213
Author:Paul W. Zitzewitz
Publisher:Paul W. Zitzewitz
Chapter1: A Physics Toolkit
Section: Chapter Questions
Problem 60A
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question about how the author got the equation in the red box from, as it makes no sense

Part B The same system is being used as in part a but this time the mass m is being pulled down with a force as can be seen in the figure below. Find the equation of motion for this system where m is the mass, k is the stiffness of the spring, x is the displacement and t is the time. I m Fsin(at) F Also, show that x = Acos (wt) + Bsin(wt) + k-ma² sin (at) where A, B are constants and w = A m Transcribed Image Text: Also, show that X = Acos (wt) + Bsin(wt) + constants and w=k}m Fsin(at) m F k-ma² sin (at) where A, B are
Transcribed Image Text:Part B The same system is being used as in part a but this time the mass m is being pulled down with a force as can be seen in the figure below. Find the equation of motion for this system where m is the mass, k is the stiffness of the spring, x is the displacement and t is the time. I m Fsin(at) F Also, show that x = Acos (wt) + Bsin(wt) + k-ma² sin (at) where A, B are constants and w = A m Transcribed Image Text: Also, show that X = Acos (wt) + Bsin(wt) + constants and w=k}m Fsin(at) m F k-ma² sin (at) where A, B are
Now, let, x=D Sin (xt) ; D- constant Substituting this into the equation of motion, - (1) D Sin (1) + (+) sin (-1) = - (D) x + (1) +xt) - (km) D D+ F-KD = F M - D F = - =>>> D 1 So, K-x²m F sin(at) x = Acas (wt) + Bsm (wt) + ((x = x²)) sin (ext) Comparing this equation with the desired form, A = 0, B = 0, K = F+m Now, x= A cos (W)+ BSin (wt) +- F K-ma² Sin(at) [Prored]
Transcribed Image Text:Now, let, x=D Sin (xt) ; D- constant Substituting this into the equation of motion, - (1) D Sin (1) + (+) sin (-1) = - (D) x + (1) +xt) - (km) D D+ F-KD = F M - D F = - =>>> D 1 So, K-x²m F sin(at) x = Acas (wt) + Bsm (wt) + ((x = x²)) sin (ext) Comparing this equation with the desired form, A = 0, B = 0, K = F+m Now, x= A cos (W)+ BSin (wt) +- F K-ma² Sin(at) [Prored]
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