4. A mass attached to a spring hanging from the ceiling is pulled down 10 cm from its rest position and released. The amplitude decreases by 5% each second and the spring oscillates 3 times each second. Find the damping constant c rounded to 4 decimal places. Then find a function D(t) that gives the distance of the mass from equilibrium at t seconds after the mass was released.

Nilo

A mass is suspended from a spring and is pulled down 3 cm from equilibrium and released. It completes a period in 2 seconds. Ignoring damping factors, find the function for the displacement from equilibrium h(t) in centimeters t seconds after the mass is released.

When an object with a mass of 5 kg is connected to the end of a spring, the spring extends 10 meters and reaches equilibrium. This spring-mass system is placed in an environment with a damping constant of 5 kilograms/second, and the mass is pulled down √ 3 meters from the equilibrium position and released without initial velocity. Find the function that shows the time-dependent change of the position of the given damped spring-mass system. Determine the period and amplitude of the movement. Determine how many seconds it takes for the system to first pass the maximum position (in the positive or negative direction) and the equilibrium position after t = 0. (gravity = 10 meters/second) Then transform the equation of the mass-spring system into a system of equations and draw a sample orbit by creating the vector field of the system and interpret the shape of this orbit.