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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- 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? ftA 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? ft
- A mass weighing 10 pounds stretches a spring 0.25 ft. This mass is removed and replaced with a mass of 1.6 slugs, which is released 1/3 foot above the equilibrium position with a downward speed of 5/4 ft/sec. Find the equation of motion.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 seconds
- A shell of mass 4 kg is shot upward with an initial velocity of 200 m/sec. The magnitude of the force on the shell due to air resistance is 20 the ground? What is the maximum height? Assume the acceleration due to gravity to be 9.81 m/s². When will the shell reach its maximum height above the ground? The shell will reach maximum height after 18.16 seconds. (Round to two decimal places as needed.) What is the maximum height? The maximum height is 1747 m. (Round to the nearest whole number as needed.) 3 (...) When will the shell reach its maximum height aboveA cylinder is fitted with a piston, beneath which is a spring, as in the drawing. The cylinder is open to the air at the top. Friction is absent. The spring constant of the spring is 3700 N/m. The piston has a negligible mass and a radius of 0.031 m. (a) When the air beneath the piston is completely pumped out, how much does the atmospheric pressure cause the spring to compress? (b) How much work does the atmospheric pressure do in compressing the spring?