A mass of 3kg stretches a spring 40cm. Suppose the mass is displaced an additional 12em in the positive (downwardi direction and then ruleased. Suppose that the damping constant is 2 N/m and assume g 9.8 m/s is the gravitational accelaration Set up a differential equation that describes this system. Let a to denote the displacement, in metern, of the mas from its equlibrium position, and give your answer in terms of a,e', a". 3" + 2 +245r 0 (b) Enter the intial conditions z(0) -12 m. z'(0) 0 m/s o ls this wyotem under damped, over damped, or critically damped? under damped

A mass of 3kg stretches a spring 40cm. Suppose the mass is displaced an additional 12em in the positive (downwardi direction and then ruleased. Suppose that the damping constant is 2 N/m and assume g 9.8 m/s is the gravitational accelaration Set up a differential equation that describes this system. Let a to denote the displacement, in metern, of the mas from its equlibrium position, and give your answer in terms of a,e', a". 3" + 2 +245r 0 (b) Enter the intial conditions z(0) -12 m. z'(0) 0 m/s o ls this wyotem under damped, over damped, or critically damped? under damped

Physics for Scientists and Engineers: Foundations and Connections

1st Edition

ISBN:9781133939146

Author:Katz, Debora M.

Publisher:Katz, Debora M.

Chapter16: Oscillations

Section: Chapter Questions

Problem 8PQ: The expression x = 8.50 cos (2.40 t + /2) describes the position of an object as a function of time,...

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The expression x = 8.50 cos (2.40 t + /2) describes the position of an object as a function of time, with x in centimeters and t in seconds. What are the a. frequency, b. period, c. amplitude, and d. initial phase of the objects motion? e. What is the position of the particle at t = 1.45 s?
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An object is attached to a coiled spring. The object is pulled down (negative direction from the rest position) 5 centimeters, and then released. Write an equation for the distance d of the object from its rest position, aftert seconds if the amplitude is 5 centimeters and the period is 7 seconds. The equation for the distance d of the object from its rest position is (Type an exact answer, using t as needed. Use integers or fractions for any numbers in the equation.) Enter your answer in the answer box. Save for Later 6:03 PM 11/14/2020 P Type here to search Pgup PgDn F12 End PrtScn F8 Home F9 F11 F10 DII F6 F7 Esc F3 F4 F5 F1 F2 & 23 24 5 6 7 8 1 2 3 4. P Y U Q W E R 60 T
A mass of 10 kilograms is attached to the end of a spring. A force of 4 Newtons stretches the spring 10 cm. The mass is pulled 15 cm above the equilibrium point and then released with an initial downward velocity of 20 cm/sec. Determine the displacement of the mass as a function of time. Spring constant: Differential Equation and initial conditions: whose consta 50 cm/sec. Determine Displacement of the mass as a function of time: Niem. The system i
It is known that a general solution for the position of a harmonic oscillator is x(t) = C cos (wt) + S sin (wt), where C, S, and ware constants. (Figure 2) Your task, therefore, is to determine the values of C, S, and w in terms of k, m,and init and then use the connection between x (t) and a (t) to find the acceleration. Figure L min x=0 Xinit 1 of 2 > Part A Combine Newton's 2nd law and Hooke's law for a spring to find the acceleration of the block a (t) as a function of time. Express your answer in terms of k, m, and the coordinate of the block x (t). ► View Available Hint(s) a (t) = Submit 17 ΑΣΦ Part B Complete previous part(s) Review | Constants ?
Suppose a spring with spring constant 2 N/m is horizontal and has one end attached to a wall and the other end attached to a 2 kg mass. Suppose that the friction of the mass with the floor (i.e., the damping constant) is 4 N. s/m. Set up a differential equation that describes this system. Let x to denote the displacement, in meters, of the mass from its equilibrium position, and give your answer in terms of a, x', ". Assume that positive displacement means the mass is farther from the wall than when the system is at equilibrium. help (equations) Find the general solution to your differential equation from the previous part. Use c₁ and c₂ to denote arbitrary constants. Use t for independent variable to represent the time elapsed in seconds. Enter c₁ as "c1" and c₂ as "c2". Your answer should be an equation of the form x =?. help (equations) Is this system under damped, over damped, or critically damped?? Enter a value for the damping constant that would make the system critically…
An object is attached to a coiled spring. The object is pulled down (negative direction from the rest position) 8 centimeters, and then released. Write an equation for the distance d of the object from its rest position, after t seconds if the amplitude is 8 centimeters and the period is 6 seconds. The equation for the distance d of the object from its rest position is (Type an exact answer, using x as needed. Use integers or fractions for any numbers in the equation.) Enter your answer in the answer box. Save for Later 10:02 PM 4) 11/15/2020 Type here to search PgUp F11 PgDn F12 End Home F9 PrtScn DII F10 In F4 F5 F6 F7 F8 F1 F2 F3 2$ & 2 4. 5 6 7 8 E Y U P T R 3. W/
An object is attached to a coiled spring. The object is pulled down (negative direction from the rest position) 9 centimeters, and then released. Write an equation for the distance d of the object from its rest position, after t seconds if the amplitude is 9 centimeters and the period is 6 seconds. The equation for the distance d of the object from its rest position is (Type an exact answer, using z as needed. Use integers or fractions for any numbers in the equation.) (? Enter your answer in the answer box. Save for Later 3:18 PM O Type here to search O 11/15/2020 PgUp PgDn F12 DII PrtScn Home F9 End F10 F11 Ins F4 F5 F6 F7 F8 F1 F2 F3 2$ & ) %23 %3D 3. 4. 5 6 7 8 E R Y U | [ T
MärkxsfH) Problem 1: A mass of 20 grams stretches a spring by 10/169 meters. (a) Find the spring constant k, the angular frequency w, as well as the period T and frequency f of free undamped motion for this spring-mass system. (b) Find the general solution x(t) of the DE for the free spring-mass system. (c) Suppose that an exterior force of F(t) = 2.5 sin(12t) in Newtons acts on the spring-mass system. Find the equation of motion (the solution x(t)) of the system if the mass initially is at rest in its equilibrium position.