Question

Mass weighing 20 pounds stretches a spring 6 inches. The mass is initially released from rest from a point 6 inches below the equilibrium position

. (a) Determine the equation of motion.
(b) Find the position of the mass at the time t = masis, s, and s.
(c) What is the velocity of the mass when t = п/12 , Зп/16,п/6sп/4s? In which direction is the mass heading at this instant?
(d) At what time does the mass pass through the equilibrium position?|

Answer 1

To determine the equation of motion for the given scenario, use Hooke's law and the equation of motion for a mass-spring system.

Step-by-step explanation:

To determine the equation of motion for the given scenario, we need to use Hooke's law, which states that the force exerted by a spring is directly proportional to the displacement from its equilibrium position. The equation of motion for a mass-spring system is:

m*d^2x/dt^2 + k*x = 0

where m is the mass, x is the displacement from the equilibrium position, t is time, and k is the force constant of the spring.

To find the position, velocity, and acceleration of the mass at a specific time t, you can use the equation of motion in conjunction with initial conditions, such as the initial displacement and velocity of the mass.