Hi, just wanted to see if you guys could help me with these problems. a spring w

Question

Hi, just wanted to see if you guys could help me with these problems.

a spring with a spring constant of 12 pounds per foot is attached to the ceiling. A 4 pound weight is attached. How far does the spring stretc The mass-spring system is set in motion in a medium that imparts a damping force numerically equal to 2 times the velocity. The mass is pushed up 3 inches from the equilibrium position and given a downward velocity of 2 feet per second. Write down and solve the initial value problem for the position x(t) as a function of time, t. Solve the initial value problem

Explanation / Answer

The angular frequency of a mass on a spring is: omega = 2 pi / T = sqrt (k/m) Solve for the spring constant: k = 4 pi^2 m / T^2 At equilibrium, the spring force equals the weight: F = kx = mg Solve that for the distance of stretch between the hanging mass at equilibrium and the unloaded spring: x = mg / k = g T^2 / 4 pi^2

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