find a model for simple harmonic motion if the position at t = 0 is 6, the amplitude is 6 centimeters, and the period is 4 seconds

y = 6cos (π/2) t

Step-by-step explanation:

Given in the question that,

in a simple harmonic motion in which

at t=0 the amplitude is 6 cm, so the simple harmonic motion will be in cosine form. As in case of sine function, the value of function at t=0 is 0.

And,

the period is given as 4 sec

We know that model equation of simple harmonic motion is

y = a. cosb (t + c) + d

here,

a is amplitude

c is Horizontal shift or phase shift

d is Vertical shift

Step1Find b

Period = 2 π / b

4 = 2π / b

b = 2π/4

b = 1π/2

Step2Find shifts

Horizontal and vertical shifts are 0.

So, c = 0 and d = 0

Step3Plug those values in the above in the equation

y = 6cos π/2 (t + 0) + 0

y = 6cos (π/2) t