Understanding SHM Equations: Solving Two Equations and Identifying Mistakes

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Homework Statement


Printed multiple-choice question 5: two equations y = 2A cos²ωt and y = A(sin ωt + √3 cos ωt), with options A to D about SHM, maximum speeds and accelerations.


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 ?
 
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  • Printed multiple-choice question 5: two equations y = 2A cos²ωt and y = A(sin ωt + √3 cos ωt), with options A to D about SHM, maximum speeds and accelerations.
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Jahnavi said:
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.

Jahnavi said:
This makes Option 3) correct .

But given answer is option 2) .

What is the mistake ?
Option C is correct.
 
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