Question

Function $x = A sin ^2 \omega t + B cos^ 2 \omega t + C sin \omega t cos \omega t$ represents SHM

• A. For any value of A , B and C (except C = 0)
• B. If $A= - B,C = 2B, \, \, amplitude \, \, = | B \sqrt 2 |$
• C. If $A = B ; C = 0$
• D. If $A = b : C = 2b, \, \, amplitude \, \, = |B |$

Answer 1

Answer: (D)

If $A = b : C = 2b, \, \, amplitude \, \, = |B |$

Answer 2

For A = - B and C = 2B
$X =B cos 2 \omega t + B sin 2 \omega t = \sqrt 2 B sin\bigg( 2 \omega t +\frac{\pi}{4} \bigg)$
This is equation of SHM of amplitude $\sqrt 2 B$
.
If A = B and C = 2B , then $X = B + B sin 2 \omega t$
This is also equation of SHM about the point X = B. Function
oscillates between X = Oand X = 2B with amplitude B.