17 In questions 1, find the function that shows the time dependent change ofthe position of the given undamped spring-mass system. Determine theperiod and amplitude of the motion. Determine how many seconds after t =0 the system first passes the maximum position (in the positive or negativedirection) and the equilibrium position. (You will find the spring constant kyourself. Please make sure that the units you use are compatible with eachother. For simplicity, you can use seconds as time units, kilograms as massunits, meters as displacement units. For gravitational acceleration, you canuse g = 10 m/s². Get help from the calculator in your transactions.)1. A massless spring, when a mass of 50 grams is attached to its end, moves10 centimeters down from its equilibrium position and stays in balance inthis position. This spring-mass system is pulled down 0.2 meters from thisnew equilibrium position and released at the first speed.Go to https://www.geogebra.org/m/utcMvuUy website. After transforming theproblem you solved in question 1 into a differential equation system, enter thesystem in the "x'(t)" and "y'(t)" boxes on the upper left side of the interactivewindow in the site content, and then click somewhere on the window to draw thephase diagram of the system. . While the phase diagram is being drawn, take theprintout of the page and indicate the direction in which time is flowing by drawingan arrow with your pen. Then, mark the following moments on the diagram with apencil, denoted by the period T of the mass-spring system you solved in Question 1:- moment t=0- The first moment when the mass-spring system passes the maximum amplitudeafter t=0- The first moment when the mass-spring system passes the minimum amplitudeafter t=0- The first moment in which the mass-spring system passes the equilibrium positionafter t=0- t = T/2-t=T

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Description: 17 In questions 1, find the function that shows the time dependent change ofthe position of the given undamped spring-mass system. Determine theperiod and amplitude of the motion. Determine how many seconds after t =0 the system first passes the maxi

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In questions 1, find the function that shows the time dependent change of the position of the given undamped spring-mass system. Determine the period and amplitude of the motion. Determine how many seconds after t = 0 the system first passes the maximum position (in the positive or negative direction) and the equilibrium position. (You will find the spring constant k yourself. Please make sure that the units you use are compatible with each other. For simplicity, you can use seconds as time units, kilograms as mass units, meters as displacement units. For gravitational acceleration, you can use g = 10 m/s². Get help from the calculator in your transactions.) 1. A massless spring, when a mass of 50 grams is attached to its end, moves 10 centimeters down from its equilibrium position and stays in balance in this position. This spring-mass system is pulled down 0.2 meters from this new equilibrium position and released at the first speed.

In questions 1, find the function that shows the time dependent change of the position of the given undamped spring-mass system. Determine the period and amplitude of the motion. Determine how many seconds after t = 0 the system first passes the maximum position (in the positive or negative direction) and the equilibrium position. (You will find the spring constant k yourself. Please make sure that the units you use are compatible with each other. For simplicity, you can use seconds as time units, kilograms as mass units, meters as displacement units. For gravitational acceleration, you can use g = 10 m/s². Get help from the calculator in your transactions.) 1. A massless spring, when a mass of 50 grams is attached to its end, moves 10 centimeters down from its equilibrium position and stays in balance in this position. This spring-mass system is pulled down 0.2 meters from this new equilibrium position and released at the first speed.

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Concept explainers

Simple harmonic motion

Simple harmonic motion is a type of periodic motion in which an object undergoes oscillatory motion. The restoring force exerted by the object exhibiting SHM is proportional to the displacement from the equilibrium position. The force is directed towards the mean position. We see many examples of SHM around us, common ones are the motion of a pendulum, spring and vibration of strings in musical instruments, and so on.

Simple Pendulum

A simple pendulum comprises a heavy mass (called bob) attached to one end of the weightless and flexible string.

Oscillation

In Physics, oscillation means a repetitive motion that happens in a variation with respect to time. There is usually a central value, where the object would be at rest. Additionally, there are two or more positions between which the repetitive motion takes place. In mathematics, oscillations can also be described as vibrations. The most common examples of oscillation that is seen in daily lives include the alternating current (AC) or the motion of a moving pendulum.

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The motion of a mass and spring is described by the following equation: 11y"+4y+6y= 35 cos(yt) Identify the value of y that would produce resonance in the system. Give an exact value, but you don't need to simplify radicals. Y What is the amplitude of the steady-state solution when the system is at resonance? Round your answer to two decimal places. The amplitude is If there was no external force, the oscillation of the spring could be described in the form A sin(ßt + p). What is the value of B? Give an exact value, but you don't need to simplify radicals. В
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 ?
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If you did the previous question right, you hopefully got an expression for yo. You may notice that you can simplify the differential equation a little bit: d'y k (y – yo) dt2 т The parameter yo now plays the roll of the "relaxed length". A better term may be "equilibrium value for y". But mathematically, it's identical to a relaxed length with the spring as the only force. We continue using this equation: y(t) = Y0 + A cos(wt + y) Now, solve for A (in cm) with these parameters. Again, if you need more information, enter -100000. The parameters are: •m = 200 grams • Yo = (equilibrium value) = 40 cm • k = (spring constant) = 0.03 N/cm
Oscillations
Two blocks and three springs are Configured below. All motion is honzental. when the blocks are aū jest spoings are unstretched: Kz k3 Suppse mi=2m mzzm, K,=4k okzz k, Ksz 2k. Find the charactesistics freguencies Foo Small oscillations.
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A block oscillating on a spring has period T = 2.4 s . Note: You do not know values for either m or k. Do not assume any particular values for them. The required analysis involves thinking about ratios. a)What is the period if the block's mass is quadrupled? b)What is the period if the value of the spring constant is doubled? c)What is the period if the oscillation amplitude is halved while
Let’s think about the energy of the system a little bit more. Imagine there is damping (frictional) force acting on the mass as well. (That is, there is a force removing energy from the system.) How would this impact the parameters of oscillation, the period, and amplitude? Make a rough sketch of what you would expect the behavior of damped oscillation to look like and how it would be different from SHM.