me are modeled by the differential equation, 1) (0) Recall that spring mass systems are mos...
A force of 720 newtons stretches a spring 3 meters. A mass of 60 kilograms is attached to the end of the spring and is initially released from the equilibrium position with an upward velocity of 6 m/s. Find the equation of motion.
please solve both. thank you! A mass of 1.25 kg stretches a spring 0.06 m. The mass is in a medium that exerts a viscous resistance of 56 N when the mass has a velocity of 2 . The viscous resistance is proportional to the speed of the object. Suppose the object is displaced an additional 0.03 m and released. Find an function to express the object's displacement from the spring's equilibrium position, in m after t seconds. Let positive...
In problems 14-17, set up the spring mass equation. Determine whether it is undamped, under, critically or overdamped. Solve the IVP and draw a graph (technology is cool) of the solution on the interval 0 < t < 12. If the system Is underdamped convert the solution to the form Re^alpha t sin(beta t + delta) A mass weighing 64 pounds stretches a spring 0.32 foot. The mass is initially released from a point 8 inches above the equilibrium position...
The differential equation describing the motion of a mass attached to a spring is x'' + 16x = 0. If the mass is released at t = 0 from 1 meter above the equilibrium position with a downward velocity of 3 m/s, the amplitude of vibrations is Please show all work. Thank you!
Differntial Equations Forced Spring Motion 1. A 1 kg mass is attached to a spring of spring constant k = 4kg/82, The spring-mass system is attached to a machine that supplies an external driving force of f(t) = 4 cos(wt). The systern is started from equilibrium i.e. 2(0) = 0 and z'(0) = 0. There is no damping. (a) Find the position x(t) of the mass as a function of time (b) write your answer in the form r(t)-1 sin(6t)...
differential equation 01 /8 points l Previous Answers 11 5.1.005 stretches a spring 6 inches. The mass is initially released from rest from a point 9 inches below the equilibrium position 2 s. (Use g 32 ft/s' for the acceleration due to gravity.) (a) Find the position x of the mass at the times t π/12, m/8, π/6, π/4, and 9m/3 x(n/12) x(T/8) ft ft x(T/4) x(9m/32)- (b) What is the velocity of the mass when t3/16 s? ft ft/s...
Differential Equation problem We know that a force of 2.8 Newtons is required to stretch a certain spring 0.7 meters beyond its natural length. A 1.44-kg mass is attached to this spring and allowed to come to equilibrium. The mass-spring system is then set in motion by applying a push in the upward direction that gives the mass an initial velocity of 1.04 meters per second. Let y(t) represent the displacement of the mass above the equilibrium position t seconds...
This Is Math Differential Equation Please Show Your Work Clearly and Short. Thank You! 2. (7 pts) A mass weighing 20 pounds, attached to the end of a spring, stretches it 8 inches. Initially the mass is released from 3 inches above the equilibrium position with a downward velocity of 3 feet per second. Find the equation of motion. 2. (7 pts) A mass weighing 20 pounds, attached to the end of a spring, stretches it 8 inches. Initially the...
mass weighing W pounds stretches a spring 7 foot and stretches a different spring foot. The two springs are attached in series and the mass is then attached to the double spring as shown in the figure below. (a) A rigid suppont that the motion is free and that there is no damping force present. Determine the equation of motion if the mass is initially released at a point 1 foot below the equlbrium postion with a downward velocity of...
(a) A mass weighing w pounds stretches a spring spring as shown in the figure below foot and stretches a different spring foot. The two springs are attached in series and the mass is then attached to the double rigid support Assume that the motion is free and that there is no damping force present. Determine the equation of motion if the mass is initially released at a point 1 foot below the equilibrium position with a downward veloity of's...