Emerson was one of a small community of influential thinkers around his home of concord, massachusetts, known as :

It is known as Transcendentalism. Transcendentalism is an American scholarly, political, and philosophical development of the mid-nineteenth century revolved around Ralph Waldo Emerson. Transcendentalism is a philosophical development that created in the late 1830s in the eastern United States. It emerged as a response to or challenge the general condition of intellectualism and the deep sense of being at the time.

Step-by-step explanation:

Let the function be a cosine function

H(t)= A cos(B(t+C)) + D

Average height = -20 cm

The object's maximum and minimum heights are each 5 cm from its average height. Therefore:

Maximum Height,

Minimum Height ,  

The amplitude, A is denoted by :

The vertical shift, D is denoted by :

The period T is given by,

T=2 seconds

The phase shift , C is given by:

C=-0.2 (since it first achieves its average height to the right at t=0.2 sec)

Therefore, our function is defined as: