A 96-lb weight is attached to a spring with constant 12 lb/ft. Find and graph the steady state component of the displacement if the mass is subjected to an external force F(t) = 18 cost - 9 sint lb and a shock absorber supplies 24 lb of damping for each ft/s of velocity.
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- 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.Suppose a 1.6-oz golf ball is placed on a vertical spring with force constant k = 2 lb/in. The spring is compressed 6 in. and released. About how high does the ball go (measured from the spring’s rest position)?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
- 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. (Useg = 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? ftAn object is shot straight upward from sea level with an initial velocity of 400 ft/sec. a. Assuming that gravity is the only force acting on the object, give an upper estimate for its velocity after 5 sec have elapsed. Use g = 32 ft/sec2 for the gravitational acceleration. b. Find a lower estimate for the height attained after 5 sec.A spring is stretched 8 feet into equilibrium by an object weighing 64 pounds, with a damping force of 8 pounds per ft/sec and an ex ternal force of 24 pounds. If the object is pushed down with a speed of 4ft/sec from a position 1 ft above the equilibrium position, find its displacement.
- A sheet of water of uniform thickness (h = 0.03 m) flows from the device shown in the figure below. The water enters vertically through the inlet pipe and exits horizontally with a speed that varies linearly from 0 to 11 m/s along the 0.2-m length of the slit. Determine the y component of anchoring force necessary to hold this device stationary. FAY = 0 m/s- i 0.2m 0.03m N 11m/sAn 8 lb weight stretches a spring 2 inches. It is attached to a dashpot with damping constantc=4 lb-sec/ft. The weight is initially displaced 3 inches above equilibrium and given a downwardvelocity of 4 ft/sec. Find its displacement for t > 0.A 4 – foot spring measures 8 feet long after a mass weighing 8 pounds is attached to it. The medium through which the mass moves offers a damping force numerically equal to v2 times the instantaneous velocity. Find the equation of motion if the mass is initially released from the equilibrium position with a downward velocity of 5 ft/s. Find the time at which the mass attains its extreme displacement from the equilibrium position. What is the position of the mass at this instant?
- Find the position of the mass after t secondsA firework of mass 0.4 kg is fired vertically upwards with initial speed 40 m/s. The firework itself provides a force of 2 N upwards. The firework explodes after 6s. Find the height at which it explodes.A cylindrical tank, shown to the right, has height 8 m and radius 4 m. Suppose the water tank is half-full of water. Determine the work required to empty the tank by pumping the water to a level 6 m above the top of the tank. Use 1000 kg/m for the density of water and 9.8 m/s² for the acceleration due to gravity. 3 4 m Draw a y-axis in the vertical direction (parallel to gravity) and choose the center of the bottom of the tank as the origin. For 0 ≤ y ≤8, find the cross-sectional area A(y). A(y) = (Type an exact answer, using as needed.) 8 m
