sinusoidal function question?

Question

i really don't understand this question can someone help me

3. A scientist recorded the movement of a pendulum for 10 s. The scientist began recording when the pendulum was at its resting position. The pendulum then moved right (positive displacement) and left (negative displacement) several times. The pendulum took 4 s to swing to the right and the left and then return to its resting position. The pendulum’s furthest distance to either side was 6 in. Graph the function that represents the pendulum’s displacement as a function of time.
(a) Write an equation to represent the displacement of the pendulum as a function of time.
(b) Graph the function

Answer 1

The pendulum starts being timed at equilibrium position, this suggests you use a sine function since sin(0)=0

The time it takes to make one full revolution is what's called the period, represented by a T. You are given T= 4 sec. The distance from equilibrium is the amplitude, A of the function which is given to be 6 in.

 

General wave function:

 

f(t) = A*sin( t*2pi/T - b) + c

 

A = |amplitude| ; distance from the midpoint

T = period ; time it takes to make one full revolution

b = shifts the graph right/left

c = shifts the graph up/down

 

This graph lies right on the axis so there will be no need to shift the graph

 

 

f(t) = 6*sin(t*pi/2) 

 

y-axis will be units of inches and x-axis, seconds