A mass weighing 4 pounds is attached to a spring whose constant is 2 Ib/ft. The medium offers a damping force that is numerically equal to the instantaneous velocity. The mass is initially released from a point 1 foot above the equilibrium position with a downwardvelocity of 14 ft/s. Determine the time (in s) at which the mass passes through the equilibrium position. (Use g = 32 ft/s? for the acceleration due to gravity.)Find the time (in s) after the mass passes through the equilibrium position at which the mass attains its extreme displacement from the equilibrium position.What is the position (in ft) of the mass at this instant?ft

The spring force and the weight are identical in magnitude but opposing in direction at a certain…

Answered: A mass weighing 4 pounds is attached to…

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Determine the natural frequency of the spring- mass system in both radians per second and cycles per seconds (Hz) k = 9.72 kN/m 30 kg Own wn = 2.86 rad/s and fn Own = 0.09 rad/s and fn Own = 0.57 rad/s and fn Own = 18 rad/s and fn =
2. A body weighing 25 lb is suspended from a spring of constant k = 160 lb /ft. At time t = 0 it has a downward velocity of 2 ft /sec as it passes through the position of static equilibrium. Determine (a) the system period and (b) the maximum acceleration attained by the mass. Use 4 decimal places
3: A 24 lb weight stretches a spring 6 feet. The weight hangs vertically from the spring and a damping force numerically equal to 2√√3 times the instantaneous velocity acts on the system. The weight is released from 3 feet above the equilibrium position with a downward velocity of 14 ft/s. (a) Determine the time (in seconds) at which the mass passes through the equilibrium position. (b) Find the time (in seconds) at which the mass attains its extreme displacement from the equilibrium position.
7. Consider the pendulum-and-spring system depicted below. Here the mass of the pendulum rod is negligible. Derive the equation of motion and the natural frequency using the energy method. k m y you
A force of 3 N stretches a spring by 1 m.(a) Find the spring constant k.(b) Amass of 4 kg is attached to the spring.At t = 0,the mass is pulled down a distance 1 meter fromequilibrium and released with a downward velocityof 0.5 meters/second. Assuming that dampingis negligible, determine an expression for the positionof the mass at time t. Find the circular frequencyof the system and the amplitude, phase,and period of the motion.
A mass weighing 4 pounds is attached to a spring whose constant is 2 ib/ft. The medium offers a damping force that is numerically equal to the instantaneous velocity. The mass is initially released from a point 1 foot above the equlibrium position with a downward velacity of 12 t/s. Determine the time (in s) at which the mass passes through the equilibrium position. (Use g -32 /s for the acceleration due to gravity.) Find the time (in s) after the mass passes through the equilibrium position at which the mass attains its extreme displacement from the equilibrium position. What is the position (in t) of the mass at this instant? ft
A 225kN test aircraft moving with velocity v = Xo = 25 km/h collides with a rigid barrier at t = 0. As a result of the behaviour of its energy absorbing capabilities, the response of the aircraft to the collision can be simulated by the damped spring- mass oscillator shown with k = 3MN/m and c = 840 kN. s/m. Assume that the mass is moving to the left with a velocity vo = xo = 25 km/h and the spring is unstretched at t = 0 determine the aircraft's deceleration: a) Immediately after it contacts the barrier; b) att = 0.04s and; c) at t= 0.08s. Vo = ******** xo ****** Vo = xo www m Figure Q5 - Aircraft Collision F(t)
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A spring has a spring constant of k=18N/m, hung with a weight of mass m=½ kg. If the load is in an equilibrium position, then it is pulled and released with a speed of 3 m/s, then determine the equation of motion of the object if it does not experience friction or damping.

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