Understanding SHM Equations: Solving Two Equations and Identifying Mistakes

[Jahnavi]

Homework Statement

Homework Equations

The Attempt at a Solution

y = 2Acos²ωt = A(1+cos2ωt)

y-A = Acos2ωt . This is SHM with origin at y = A i.e at the maximum position .

Is that correct ?

Amplitude is A and angular frequency is 2ω .

y= A(sinωt+√3cosωt) = 2Asin(ωt+π/3)

Amplitude is 2A and angular frequency is ω .

Maximum speed is product of amplitude and angular frequency .

Product is same in both the cases .

This makes Option 3) correct .

But given answer is option 2) .

What is the mistake ?

 

[Orodruin]

This is SHM with origin at x = A i.e at the maximum position .

Origin is x = A, yes, but it is definitely not the maximum position of this SHM.

This makes Option 3) correct .

But given answer is option 2) .

What is the mistake ?

Option C is correct.

 

[Jahnavi]

Thanks !