The position x(t) of an object of mass m that is attached to a vertical spring with constant ofrestitution k can be determined by solving the following initial value problemma" + kr = 0r(0) = a >0 r'(0) = b > 0,where the initial conditions indicate that the object is meters below the equilibrium positionand is released with a downward velocity of b meters per second. Suppose an object of unitmass is attached to a vertical spring and is initially 1 meter below the equilibrium positionwhen propelled downward with a speed of 2 meters per second. If the spring constant ofrestitution is 1. Determine the position of the object at time t, with t in secondsr"(t) +r(t) = 0r'(0) = 2.1(0) = 1%3D(a) Determine, using only higher-order linear differential equation solving techniques, thesolution to initial value problem.

The main objective is to solve the IVP by using higher order linear differential equations…

Answered: The position x(t) of an object of mass…

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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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.
Find the position function of a particle that travels along the x-axis for t >= 0 with acceleration of a(t)=8t-5 where the velocity at t=2 is 6 in/sec and the initial position at time t=0 is -4 inches
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
(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.
this is a non homogenous equation problem solving question.
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…
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=
Please show all work!! This most likely is made to be a probelm about mx''+bx'+kx=f(t) m = mass b = friction k = spring constant
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.
Suppose that a particle moves along a straight line with acceleration defined by a(t)=t-3 where 0<t<6 (in meters per second) find the velocity and the displacement at the time t and the total distance traveled up to t=6 if v(0)=3 and d(0)=0

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