9. TA mass weighing 16 pounds stretches a spring feet. The mass is initially released from rest from a point 2 feet below the equilibrium position, and the subsequent motion takes place in a medium that offers a damping force that isnumerically equal to the instantaneous velocity. Find the equation of motion x(t) if the mass(5)driven by an external force equal to f(t) = 20 cos(3t). (Use g = 32 ft/s² for the acceleration due to gravity.)ft

A mass of weight pound is stretches a spring feet.The mass is initially released from rest from a…

Answered: 8 A mass weighing 16 pounds stretches 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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An object of mass m falling near the surface of the earth is retarded by air resistance proportional to its velocity so that, according to Newton's Second Law of Motion, dv m- mg – kv, dt where v=v (t) is the velocity of the object at time t, andg is the acceleration of gravity near the surface of the earth. Assume that the object falls from rest at time t=0, that is v (0) =0. The velocity of the object at time t=m/k is v (m/k)= (1 – e-1) OA. mg k O B. None of these
Use the concept of Particular Antiderivatives and Rectilinear Motion to answer the problem below: On the edge of an 8m building, Sam throws his toy vertically upwards at initial velocity = 28 m/s. If the only force that acts on the toy is accelerationdue to gravity (-32 ft/s), a. How many seconds will it take for the toy to reach its maximum height?b. What is the toy's speed when it hits the ground?
A mass weighing 8 pounds is attached to a spring whose constant is 4 lb/ft. The medium offers adamping force that is numerically equal to the two times instantaneous velocity. The mass is initiallyreleased from a point 1 foot above the equilibrium position with a downward velocity of 8 ft/s.(a) Specify the 2nd order DE as an IVP for the mass spring system.(b) Solve the equation to find the position of the mass at any time t.(c) Determine the time at which the mass passes through the equilibrium position.(d) Find the time at which the mass attains its extreme displacement from the equilibrium position. Whatis the position of the mass at this instant?
A mass weighing 16 pounds stretches a spring 8 feet. The mass is initially released from rest from a point 4 feet below the equilibrium position, and the subsequent motion takes place in a medium that offers a 1 damping force that is numerically equal to - the instantaneous velocity. Find the equation of motion x(t) if the mass is driven by an external force equal to f(t) = 20 cos(3t). (Use g = 32 ft/s2 for the acceleration 2 due to gravity.) x(t) = ft
A 12-lb weight stretches a spring 2 ft. The weight is pulled 8 in below theequilibrium position and given an initial downward velocity of 3 ft/sec. (Recallthat the downward direction is positive.) Find the motion of the weight as afunction of time, assuming that the damping force may be neglected. *** Please show handwritten work - thank you
Explorers on a small airless planet used a spring gun to launch a ball bearing vertically upward from the surface at a launch velocity of 15 m/sec. Because the acceleration of gravity at the planet’s surface was gs m/sec2, the explorers expected the ball bearing to reach a height of s = 15t - (1/2)gs t2 m t sec later. The ball bearing reached its maximum height 20 sec after being launched. What was the value of gs?
A cylindrical buoy weighing 100 lb (thus of mass m = 3.125 slugs in ft-lb-s (fps) units) floats in water with its axis vertical . When depressed slightlyand released, it oscillates up and down four times every 10s. Find the radius of the buoy.
3. A girl is being pulled at the rate of 3 m/s at the instant (t = 0) when her friend released her hand. The girl then begins to skate in the same direction of the motion exerting a force of 10N. If the weight of the girl is 45kg, and the resistance (R in Newtons) is equal to 0.1v, where v is measured in m/s, find the speed of the girl after half a min.

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