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how to find the equation to derive for part c of this problem

how to find the equation to derive for part c of this problem

Principles of Physics: A Calculus-Based Text
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 14P: In an engine, a piston oscillates with simple harmonic motion so that its position varies according...
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I am lost on how to find the equation to derive for part c of this problem. Though the solution a solution is offered (to take dv/dt by substituting t=0 into VI) no equation is given for eq. VI. I'm unable to work backwards from -17.3cm/s², and would appreciate some guidance.

Chapter 15: 4. In an engine, a piston oscillates with simple harmonic 4. w motion so that its position varies according to the expression A cos (uti Ø) a) X= 5 cos (2(0)+ T 5 cos TV6=4.999cm=X x = 5.00 cos where x is in centimeters and t is in seconds. At t = 0, find (a) the position of the particle, (b) its velocity, and (C) its acceleration. Find (d) the period and (e) the amplitude of the motion. b V= X= =A cos (2t, Ø)= 2A[-Sin (2t• Ø)] = -2:5 Sin(2t. T/6)> du e) amplade- A= Scm
Transcribed Image Text:Chapter 15: 4. In an engine, a piston oscillates with simple harmonic 4. w motion so that its position varies according to the expression A cos (uti Ø) a) X= 5 cos (2(0)+ T 5 cos TV6=4.999cm=X x = 5.00 cos where x is in centimeters and t is in seconds. At t = 0, find (a) the position of the particle, (b) its velocity, and (C) its acceleration. Find (d) the period and (e) the amplitude of the motion. b V= X= =A cos (2t, Ø)= 2A[-Sin (2t• Ø)] = -2:5 Sin(2t. T/6)> du e) amplade- A= Scm
13:46 Sun Nov 8 31% non latex denta X learning pencil X www.google.co X Bic b In an engine, a X + C a bartleby.com 11 = bartleby Q Search for textbooks, step-by-step explanation.. Ask an Expert Science / Physics / Principles... / In an engine, a piston oscillates with simple harmonic motion so that its position varies acc.. : In an engine, a piston oscillates with simple harmonic motion so that its position varie... Get live help whenever you need from online tutors! Try bartleby tutor today → Expert Solution (c) To determine The acceleration of the piston. Answer to Problem 14P The acceleration of the piston is – 17.3cm/s?. Explanation of Solution Write the expression for the acceleration. dv (V) dt Use equation (II) in equation (V), a = (VI) Conclusion: Substitute t = O in equation (VI), a = -17.3m/s² Therefore, the acceleration of the piston is –17.3cm/s² .
Transcribed Image Text:13:46 Sun Nov 8 31% non latex denta X learning pencil X www.google.co X Bic b In an engine, a X + C a bartleby.com 11 = bartleby Q Search for textbooks, step-by-step explanation.. Ask an Expert Science / Physics / Principles... / In an engine, a piston oscillates with simple harmonic motion so that its position varies acc.. : In an engine, a piston oscillates with simple harmonic motion so that its position varie... Get live help whenever you need from online tutors! Try bartleby tutor today → Expert Solution (c) To determine The acceleration of the piston. Answer to Problem 14P The acceleration of the piston is – 17.3cm/s?. Explanation of Solution Write the expression for the acceleration. dv (V) dt Use equation (II) in equation (V), a = (VI) Conclusion: Substitute t = O in equation (VI), a = -17.3m/s² Therefore, the acceleration of the piston is –17.3cm/s² .
Expert Solution
Step 1

Position for simple harmonic function is given

x=5.00cos2t+π6      .....(a)

(b) v=dxdt

  =5-1×2×sin2t+π6=-10sin2t+π6     

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