Acpw - Shm (1 Viewer)

[paper cup]

A body is in simple harmonic motion with its position at a time t given by the equation x = Acos(nt + alpha) + 1
The period of the motion is pi seconds. Initially the body is at rest 2 units to the right of the origin. Find the values of A, n, alpha.

I know it really is a basic sort of question, but we only went briefly through applications of calculus.

 

[Sharky]

A body is in simple harmonic motion with its position at a time t given by the equation x = Acos(nt + alpha) + 1
The period of the motion is pi seconds. Initially the body is at rest 2 units to the right of the origin. Find the values of A, n, alpha.

Period = 2*pi/n seconds.
Therefore n = 2.

x.dot = -2Asin(2t + alpha) (differentiating with respect to 't')

Initially: x.dot = 0 when t = 0
x = 2 when t = 0

Subbing in x=2,t=0: 2 = Acos(alpha) + 1
__________________1 = Acos(alpha)____________<==(1)

Subbing in x.dot=0,t=0: 0 = -2Asin(alpha)
____________________0 = sin(alpha)___________<==(2)

Etc... now just solve these two simulataneously.

Soz, but i'm outta time. gotta go

 

[CrashOveride]

to get tan(alpha) = 0 so alpha = 0

Then by differenetiating the x' and noting to use x-1=blabla u get x'' and center should be at x=1. Then by inspection because v=0 at extremity, it starts from extremity so A =1

 

[CrashOveride]

BTW, what is Acpw?

This question, in its almost exact form plus a secondary part, featured in my trial.
Where is it from ?

 

[paper cup]

applications of calculus.

western region trial - did you do that too?