Question

Not every interpretation of direction is that "positive is down". In this problem, assume that if initial position is above equilibrium, then it is positive, and if it is below equilibrium it is negative. This assumption will have implications on the initial velocity as well. A 5 kilogram mass is attached to a spring whose constant is 2.8125 N/m, and the entire system is submerged in a liquid that imparts a damping force numerically equal to 7.5 times the instantaneous velocity. Determine the equation of motion if the mass is initially released with a downward velocity of 2 m/sec from 15 meters above equilibrium

Answer 1

The equation of motion for a mass attached to a spring in a liquid is given by the differential equation m(d^2x/dt^2) + b(dx/dt) + kx = 0, where m is the mass of the object, b is the damping coefficient, k is the spring constant, and x is the displacement from equilibrium position.

Step-by-step explanation:

The equation of motion for a mass attached to a spring in a liquid is given by the differential equation:

m(d2x/dt2) + b(dx/dt) + kx = 0,

where m is the mass of the object (5 kg), b is the damping coefficient (7.5 times the instantaneous velocity), k is the

spring constant (2.8125 N/m), and x is the displacement from equilibrium position.

To solve the equation of motion, we need to substitute the given values into the equation and find the general solution for x(t).