A 1-kilogram mass is attached to a spring whose constant is 27 N/m, and the entire system is then submerged in a liquid that imparts a damping force numerically equal to 12 times the instantaneous velocity. Determine the equations of motion if

a. the mass is initially released from rest from a point 1 meter below the equilibrium position.
b. the mass is initially released from a point 1 meter below the equilibrium position with an upward velocity of 12 m/s.

In 1859, charles darwin published the first edition of on the origin of species, which explained his observations of various groups of animals that showed great similarities but minor differences. darwin concluded that if a population of one species separates into two different populations that live in separate locations, then over the course of many generations the different populations can develop into different species. this idea predicted many future biological findings and became the basis of modern biology. darwin’s explanation for why different species exist is best described as a(n) law. theory. inquiry. hypothesis.