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.

Find the equation of motion. (Use g = 32 ft/s2 for the acceleration due to gravity.)

x(t)= ?

Step-by-step explanation:

The equation of motion for the spring-mass system is:

Where:

- Spring constant, in .

- Mass, in .

The spring constant is:

The angular frequency is:

The initial condition for the system is:

The function for speed is obtained by deriving the previous function:

The following expressions are formed by substituting all known variables:

The phase angle is found by dividing the initial velocity by the initial position:

The amplitude is:

The equation of motion is:

answer:   x = 3 + √11     and     x = 3 - √11

step-by-step explanation:

x² - 6x + 9 = 11

(x - 3)² = 11

x - 3 = ±√11

    x = 3 ± √11

x = 3 + √11     and     x = 3 - √11