Find a model for simple harmonic motion if the position at t=0 is 5 centimeters, the amplitude is 5 centimeters, and the period is 4 seconds. a) d=5cos(4t) b) d=5sin(pi/2t) c) d=4sin(5t) d) d=5cos(pi/2t)

Step-by-step explanation:

As at t=0 the amplitude is 5 cm, so the simple harmonic motion will be in cosine form. As in case of sine function, the value of function at x=0 is 0.

We know that, in the function

As in this case the amplitude is given to be 5, hence

Also the period is given as 4, so

As nothing is given about the horizontal and vertical shift, so putting , the function becomes,

or

As in x axis time is taken as t and in y axis distance is taken as d, so the function becomes,

it's