A 1-kilogram mass is attached to a spring whose constant is 14 N/m, and the entire system is then submerged in a liquid that imparts a damping force numerically equal to 9 times the instantaneous velocity.Determine the initial conditions and equations of motion if the following is true.(a) the mass is initially released from rest from a point 1 meter below the equilibrium positionx(0) =x'(0)=x(t) ==m/s(b) the mass is initially released from a point 1 meter below the equilibrium position with an upward velocity of 13 m/sx(0) =x'(0)x(t) =mmm/sm

for spring mass problems there equations for the different situations are given as follows no…

Answered: A 1-kilogram mass is attached to a…

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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Suppose a 10-lb object stretches a spring 2.25 feet while in equilibrium. If the object is displaced an additional 1 inches and is then set in motion with an initial upward velocity of -0.7 feet per second. Use 1 slug = 32 lbs. Your answer is partially correct. (i) For what values of a, ß, and y is this spring-mass system expressed as the following initial value problem, where u (t) is the position of the object at any time t: α = eTextbook and Media ,B = = u" + au = 0, u (0) = ß, u' (0) = y? , Y = = -0.7
Find the solution to the Initial Value Problem describing the horizontal motion of a mass attached to a spring, mx = -k(x - 1), x(0)=4, x(0) = 0, for m 1, k = 9, 14. Describe in words the motion of the mass.
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
A mass weighing 16 lb stretches a spring 1/4 feet. The mass is attached to a viscous damper with a damping constant of 2 lb-s/ft and is set in motion from its equilibrium position with a downward velocity of 1/2 ft/s. a) Set up the initial value problem (differential equation). b) Solve the equation to find the position of the mass y at any time t. c) Determine when the mass first returns to its equilibrium position. Assume that the y-axis is directed downward.
(1) A mass weighing 4 lb stretches a spring 2 in. Suppose that the mass us displaced an additional 6 in. and then released. The mass is in a medium that exerts a viscous resistance of 6 lb when the mass has a velocity of 3 ft/sec. Set up the initial value problem that describes the motion of the mass.
3. A projectile is fired with an initial velocity of 128 ft/s from a cannon at time t = 0 from a height of 32 ft above the ground and at an angle of 30° with the horizontal. (a) Determine: x '(0) and y'(0). (These values represent the horizontal and vertical components of the initial velocity vector.) (b) Use integration to determine the position equations: x(t) and y(t) for the projectile t seconds after being fired by assuming that the projectile is in freefall. Thus, x"(t)=0 ft/s² and y"(t)=-32 ft/s² for all t≥ 0. (Note: x"(t) and y"(t) are the horizontal & vertical components of the projectile's acceleration vector at time t.) (c) Determine the maximum height, H, of the projectile and its horizontal distance, D, from the launch site at the time that it achieves this height. (Hint: The maximal height is attained at the time, t*, at which y'(t*) = 0.) (d) Determine the range of the projectile, R. YA (0,32) - P. 32' 128 0=30° x'(0) y'(0) H R Pr=(x(t), y(t)) is the position of the…
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.
The motion of a mass-spring system with damping is governed by y"(t) + by' (t) + 64y(t) = 0; y(0) = 1, y' (0) = 0. Find the equation of motion and sketch its graph for b = 0, 10, 16, and 20.
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.
Given the equation of state of a PVT system is bT² √P Where b is a constant. V = (a) Calculate the thermal expansivity B =) - = (3/P) ₁ 1 (c) Express the total differential of V in terms of ß and K. (b) Calculate the compressibility K =

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