Deriving position function for object in SHM

[Callumnc1]

Homework Statement:

Please see the image below

Relevant Equations:

x(t) = Acos(wt + ϕ)

For this problem,

How did they get that formula shown?

My working is,

All the solutions wrote was,

Many thanks!

 

[haruspex]

Your working headed off into a blind alley. You know that you need to be eliminating A, so tucking it inside an arccos function isn’t going to get you there.
Start by writing all three initial state equations: position, velocity and acceleration. Then see how you can combine them to eliminate one of the unknowns.

 

[Orodruin]

Please type out your work instead of attaching pictures. The pictures make it impossible to quote particular sections.

Edit: I suggest you change your unknowns from A and phi to something more direct.

 

[Callumnc1]

Your working headed off into a blind alley. You know that you need to be eliminating A, so tucking it inside an arccos function isn’t going to get you there.
Start by writing all three initial state equations: position, velocity and acceleration. Then see how you can combine them to eliminate one of the unknowns.

Thank you @haruspex and @Orodruin! I have solved the problem now.

Many thanks!

 

[haruspex]

Thank you @haruspex and @Orodruin! I have solved the problem now.

Many thanks!

You are welcome. But did you understand my comment about heading off into a blind alley? Recognising which directions cannot lead anywhere is a useful skill to develop.

 

[Callumnc1]

You are welcome. But did you understand my comment about heading off into a blind alley? Recognising which directions cannot lead anywhere is a useful skill to develop.

Thanks @haruspex! I did understand your comment, which I agree, would be very useful skill to have!

Many thanks,
Callum