Africtionless spring with a 7-kg mass can be held stretched 0.2 meters beyond its natural length by a force of 60 newtons. If the spring begins at its equilibrium position, but a push gives it an initial velocity of 1 m/sec, find the position of the mass after t seconds.

A force of 13 pounds stretches a spring 1 foot. A mass weighing 6.4 pounds is attached to the spring, and the system is then immersed in a medium that offers a damping force numerically equal to 1.6 times the instantaneous velocity. (a) Find the equation of motion if the mass is initially released from rest from a point 1 foot above the equilibrium position. (b) Express the equation of motion in the form  (c) Find the first time at which the mass passes through the equilibrium position heading upward. (Round your answer to three decimal places.)

A mass weighing 16 pounds stretches a spring 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/s? for the acceleration due to gravity.) x(t) = ft

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 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.)

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…

A 20-lb weight suspended from the end of a vertical spring stretches it 6 in. Assuming no external forces and no air resistance, find the position of the weight at any time if initially the weight is pulled down 3 in. and given an initial velocity of 2 ft/s downward.