A spring has a natural length of 10 feet, and when an 64lb weight is attached, the spring measures 13.2 feet. The weight is initially displaced 4 feet above equilibrium and given a downward velocity of 3 ft/sec. Find its displacement for t>0 if the medium resists the motion with a force of two Ibs for each ft/sec of velocity.

Find the position of the mass after t seconds

(1) The T-shaped bar is loaded with two forces and a moment as shown. The bar is supported by a pin at O and a roller at C. The mass of the bar is negligible. (a) For P = 100 N, determine the normal force at roller C and the magnitude of the reaction at pin O. (b) Determine the maximum load Pmax that can be applied for the T-shaped bar to maintain equilibrium. Ans: (a) Nc=240 N, O=116.6 N (b) Pmax = 260 N A 60 mm 24 N-m D 60 mm 40 mm B 180 N 40 mm

A force of 9 lb is required to keep a spring compressed to ft shorter than its equilibrium length. What is its spring constant? k = lb/ft

A mass weighing 24 pounds, attached to the end of a spring, stretches it 4 inches. Initially, the mass is released from rest from a point 8 inches above the equilibrium position. Give the initial conditions. (Use g = 32 ft/s2 for the acceleration due to gravity.)

A helicopter flies over the arctic ice pack at a constant altitude, towing an airborne  147-kg laser sensor which measures the thickness of the ice (see the drawing). The helicopter and the sensor move only in the horizontal direction and have a horizontal acceleration of magnitude  2.54 m/s2. Ignoring air resistance, find the tension in the cable towing the sensor.

If it takes a force of 86 Newtons to stretch a spring 9 meters from its equilibrium state, what is the spring constant k? (Round your answer to one decimal place.)

Imagine a diver jumping off a spring board that is 10 feet above the water. The board throws the diver up with an upward velocity of 9 feet per second. That means that if there were no gravity, the diver would keep going up at the rate of 9 feet every second. Fortunately for the diver, there is gravity. Eventually, gravity over comes the force of the diving board and the the diver begins to come down. So over all, the diver is thrown into the air fairly quickly, he slows down until he stops, then begins to come back down (slowly at first, then faster and faster until he hits the water). The height of any object like the diver that is projected into the air can be modeled with the following function: h(t) = -16t^2 + v*t + m In this function: h(t) is the height of the object t seconds after it was thrown into the air. t is the number of seconds after the object was thrown in the air. v is the initial upward velocity (for the diver this was 9 ft per second). m is the initial height of the…

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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 downward velocity of 16 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