4. What type of motion isbeing exhibited by the spring-mass system if B = 0?O Under-dampedO UndampedCritically-dampedO overdamped Consider the following system: A 3lbweight on a spring stretches it 6inches. Assuming a damping forcein pounds numerically equal to Bv,where v is the instantaneousvelocity in ft/sec, is present.

We can form differential equations for the spring-mass system and solve it to find the solution but…

Answered: 4. What type of motion is being…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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1. A spring is such that a 4-lb weight stretches the spring 0.40 ft. The 4-lb weight is attached to the spring (suspended from a fixed support) and the system is allowed to reach equilibrium. Then the weight is started from equilibrium position with an imparted upward velocity of 2 ft/sec. Assume that the motion takes place in a medium that furnishes a retarding force of magnitude numerically equal to the speed, in feet per second, of the moving weight. Determine the position of the weight as a function of time. 2. Find the Laplace transform of a) t² sinkt b) tsinkt 3. Find the Inverse Laplace transform of : 5s-2 s² (s+2) (S-1) S b) (s²+²)(s²+b²) a² + b², a²b², ab 0 4. Use the Laplace Transform method to solve the given system dx dy (a) 2x - y = 6e³t, dt dt 2x-3x+ x(0) = 3, d²₂ dy dt² dt dx -x+ dt dx + 3x + - 4y + 3z = 0; dt dx x(0) = 0, (0) = 1, y(0) = 0, z(0) = 0. dt 5. Find the Fourier series to represent a function of a.) f(x) = x + 1, - 2 < x < 0, = 1, 0
A mass 3 16 hangs from a spring constant of 12 lb/sec². Suppose the mass is set in motion from its equilibrium position, and then it is released with an initial velocity of 2 ft/sec downwards. There is no damping. Then u(t) satisfies the initial value problem: ¡u” +12u=0, u(0) = 0, 32 u(0) = 0, 3 32 u" + 12u = 0, 3u" + 12u: = 0, 3u" + 12u: 0, 3u" + 12u: = 0, u(0) = 0, u(0) = 0, u(0) = 2, u' (0) = 2 u'(0) =-2 u'(0) = 2 u' (0) u'(0) : = 0 =
15)A particle is moving and has acceleration by a Ge)= 6t-4. The initial velocity is vco)=5 and the initial position is s Co) =10. %3D Find the position at t= I 2014
Suppose that a falling hailstone with density 8 = 1 starts from rest with negligible radius r = 0. Thereafter its ra- dius is r = kt (k is a constant) as it grows by accretion during its fall. Use Newton's second law-according to which the net force F acting on a possibly variable mass m equals the time rate of change dp/dt of its momentum p = mv-to set up and solve the initial value problem (mv) = mg, v(0) = 0, where m is the variable mass of the hailstone, v = dy/dt is its velocity, and the positive y-axis points downward. Then show that dv/dt = g/4. Thus the hailstone falls as though it were under one-fourth the influence of gravity.
2. A mass that weighs 64 lb stretches a spring 0.8 ft. The mass is attached to a dashpot mechanism that has a damping coefficient of 8 lb s/ft and is acted on by an external force of 60 cos(4t) lb. The mass is set in motion from its equilibrium position with no initial velocity. Let y(t) denote the displacement (in ft) of the mass from its equilibrium position after t seconds. (a) Find an initial-value problem which describes this process. (You may use the fact that g = 32 ft/s' and 1 ft=12 in.) (b) Is the system underdamped, overdamped, or critically damped? Justify your an- swer.
NEED FULLY CORRECT HANDWRITTEN SOLUTION FOR THIS..... ASAP!!!!
A spring mass system consists of a spring with spring constant k and an attached block of mass m is submerged in a liquid that produces a damping force Fr. m = 2 KG K = 36 N/m Fr 18 times the velocity of the center of mass of the block. = If the mass is initially released from rest 1m below the equilibrium position: Enter your answer in lower case, ex x"+ax'+bx=0 a. "The second degree equation that describe the motion of the center of mass of the attached block is b. The initial conditions are x(0)= c. The Arbitrary Constants that satisfy the IC's are C= the order does not matter" , x'(0)= C=
(23) two screenshots of the same page, just a run on
2) Assume that the motion of a mass-spring system with damping is governed by d+b+8y = 0, y(0) = 1, y'(0) = 0. Find the equation of motion for b = 3.
3. A big slug weighing 10 pounds stretches a spring ½ foot. The slug is removed and replaced by another slug, of mass 1.6 slugs. The slug on the spring is then taken to the bottom of the sea (where the water offers resistance that is approximately equal to the velocity of the object) and then released from a position of 1/3 foot above the equilibrium with an downward velocity of 5/4 feet per second. (a) Set up the DE for this situation and show all the steps to find the position equation for the spring. Use X for the position and t for the time. Round all values to 2 decimal places for simplicity. (b) Graph your equation from (a), labeling the axes, and use your graph to find the second time where the slug is heading downwards and passes equillibrium. Write a sentence to summarize.
A mass weighing 2 pounds stretches a spring foot. Suppose the 2 1 feet and then released. If 4 mass is pulled down an additional there is no damping, which of the following Initial Value Problems model this situation? 1 u" + 16и — 0, и(0) u'(0) = 0 2' 1 и — 2u" + 2 1 u(0) 1 4' u' (0) = 0 2' 1 2u" + 0, u(0) 1 u' (0) = 0 U = 2 2' 1 2u" + 4u — 0, и(0) — 0, и'(0) 4 1 u" + 64u = 0, u(0) u'(0) = 0 4' 1 O u" + u' + 64u 4 %3D — — 0, и(0) — 0, и'(0) 4 1 O u" + 4u' + 64u = 0, u(0) u'(0) = 0 2'
Suppose a mass spring system with damping is modeled by the IVP y+8y'+\by =0; ylos =2; y'CO) =-1 a) If you were to graph the equation of motion using a graphing that you will see on your screen. Calculator, which is the graph And why? ylt) (I) (1x) 21 2 (I1) (Iv) 2- t 2 2 b) which best deseribes this system? Explain why. mass spring (I) underdamped (II) overdanmped (m) critically damped (m) undam ped E) NONE

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4. What type of motion is being exhibited by the spring- mass system if B = 0? O Under-damped Undamped Critically-damped Overdamped