IIT JEE Advanced 2006 Paper 1

We have
x = Asin2ωt+Bcos2ωt+C‌sinωt‌cosωt
=

A

2

(1−cos2ωt) +

B

2

(1+cos2ωt) +

C

2

sin2ωt
• For A = −B; C = 2B:
x = Bcos2ωt + Bsin2ωt
which is a SHM whose amplitude is B √2.
• For A = B, C = 0, we get x = A,
which is not a SHM.
• For A = B, C = 2B:
x = B + Bsin2ωt
which is SHM whose amplitude is B.
• For any values of A, B and C (except C = 0)
x =

A+B

2

+(

B−A

2

) cos 2 ωt +

C

2

sin 2ωt
which is a SHM.