Question

honors college physics class graphing with Sinusoidal RelationshipsA quantity x that oscillates in time and can be written asx=Asin(2πtT) or x=Acos(2πtT)is called a sinusoidal function with period T. Here A is a constant. The argument of the functions, 2πt/T, where t is time, is in radians.Consider the case when the constant A=3 and T=8s . Plot the graph of x=3sin(πt/4) and the graph of x=3cos(πt/4) . Note that the values of t on the horizontal axis are given in seconds.For each plot you should graph a total of 11 points. That is for each second along the horizontal axis starting at t=0 s up to and including t=10 s . The quantity, x , at each point should be rounded to one decimal place.

Answer 1

The first sinusoidal equation of the displacement with time is,

`x=3\sin ((\pi t)/(4))`

The rounded values of x to one decimal place corresponding to the value of t are,

t x

0 0

1 2.1

2 3

3 2.1

4 0

5 -2.1

6 -3

7 -2.1

8 0

9 2.1

10 3

The graphical representation of the given equation with time t is,

The second cosine equation given is,

`x=3\cos ((\pi t)/(4))`

The value of x corresponding to the values of t is,

t x

0 3

1 2.1

2 0

3 -2.1

4 -3

5 -2.1

6 0

7 2.1

8 3

9 2.1

10 0

The graphical representation of the cosine graph is,