A simple harmonic motion is described by the displacement funtion

[misa_808]

Equation given


u(t) =0.2 cos (wt) + 0.5 sin (wt), where w=3pi rad/s and displacement is in feet.

Describe the same motion using amplitute/phase format.
Describe the same motion using complex notation
For t =0.4 sec calculate u


How do you calculate u? and how do you describe the motion using amplitute and phase format based on the equation given?

 

[granpa]

you need to show that you've made an effort to solve it yourself.

 

[HallsofIvy]

For goodness, sake, certainly you know what "evaluate a functions" means!

 

[misa_808]

sorry I am not use to this so I will post my attempt to solve the problem

 

[misa_808]

I used the equation u(t) = Asin(wt+0)

I solved for displacement first u(t) = 0.5sin(3pi)(.4sec)+ 0


u (t) = 0.0328 and that is the answer for the first question but what I don't understand it that there is a cos cosine in the inital equation. So do I have to solve the cosine too inorder to get inorder to get the displacement or I am okay with this equation u (t) = Asin (wt + 0)

 

[misa_808]

If I were to describe the motion I would draw a picture of the sinusoidal wave and let the .5 and .2 graphed together showing waves and then I would say that a b sin wt is always 90degrees ahead of acos wt. But the sum of a cos wt and b sin wt produces a sinusoid of the same frequency...is this is correct