Function $$x=A$$ $$sin2$$ ω$$t+B$$ $$cos2$$ ω$$t+C$$ $$sin$$ ωt $$cos$$ ωt represents SHM :(i) for any value of A, B and C (except$$ C $$=$$ $$0)(ii) if $$A=-$$ B; C $$=$$ $$2B$$, amplitude $$=$$ $$B2(iii)$$ if A $$=$$ B; C $$=$$ $$0(iv)$$ if A $$=$$ B; C $$=$$ $$2B$$, $$amplitude=B$$

Question

Function $$x=A$$ $$sin2$$ ω$$t+B$$ $$cos2$$ ω$$t+C$$ $$sin$$ ωt $$cos$$ ωt  represents SHM :(i) for any value of A, B and C (except$$ C $$=$$ $$0)(ii) if $$A=-$$ B; C $$=$$ $$2B$$, amplitude $$=$$ $$B2(iii)$$ if A $$=$$ B; C $$=$$ $$0(iv)$$ if A $$=$$ B; C $$=$$ $$2B$$, $$amplitude=B$$

Infinity Learn · Accepted Answer

$$x=A$$ $$sin2$$ω$$t+B$$ $$cos2$$ω$$t+C$$ $$sin$$ωt $$cos$$ωt $$x=A21-$$$$cos$$ $$2$$ω$$t+B21+$$$$cos$$ $$2$$ω$$t+C2sin$$ $$2$$ωtFor (a) : For any value of A, B and C (except$$ C $$=$$ $$0), it represents SHMFor (b) : If A $$=$$ $$-B$$ and C $$=$$ $$2B$$, , x $$=$$ B $$cos$$ ωt $$+$$ B $$sin$$ $$2$$ ωt which is SHM.For (c$$ $$): If $$A=B$$,C $$=0$$, $$x=$$ A $$=$$ constant ⇒Not a SHM.For (d) : If $$A=B$$,C $$=2B$$, x $$=$$ $$B+B$$ $$sin$$ $$2$$ ωt which is SHM.

Function $x = A \sin^{2} ωt + B \cos^{2} ωt + C \sin ωt \cos ωt$ represents SHM :
(i) for any value of A, B and C (except C = 0)
(ii) if A=- B; C = 2B, amplitude = $|B \sqrt{2}|$
(iii) if A = B; C = 0
(iv) if A = B; C = 2B, amplitude $= |B|$

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Function x=A sin2 ωt+B cos2 ωt+C sin ωt cos ωt represents SHM :(i) for any value of A, B and C (except C = 0)(ii) if A=- B; C = 2B, amplitude = B2(iii) if A = B; C = 0(iv) if A = B; C = 2B, amplitude=B

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Function $x = A \sin^{2} ωt + B \cos^{2} ωt + C \sin ωt \cos ωt$ represents SHM :
(i) for any value of A, B and C (except C = 0)
(ii) if A=- B; C = 2B, amplitude = $|B \sqrt{2}|$
(iii) if A = B; C = 0
(iv) if A = B; C = 2B, amplitude $= |B|$