The equation of simple harmonic motion may not be expressed as (each term has its usual meaning)

Question

The equation of simple harmonic motion may not be expressed as (each term has its usual meaning) (A) x=A sin (ω t+φ) (B) x=A cos (ω t-φ) (C) x=a sin ω t+b cos ω t (D) x=A sin (ω t+φ)+B sin (2 ω t+φ)

Tardigrade Admin · Accepted Answer

The fourth option is a superposition of two S.H.M.'s will different frequencies and time periods. Hence it is not a true S.H.M

Q. The equation of simple harmonic motion may not be expressed as (each term has its usual meaning)

$x = A sin (ω t + ϕ)$

$x = A cos (ω t - ϕ)$

$x = a sin ω t + b cos ω t$

$x = A sin (ω t + ϕ) + B sin (2 ω t + ϕ)$

The fourth option is a superposition of two S.H.M.'s will different frequencies and time periods. Hence it is not a true S.H.M

Q. The equation of simple harmonic motion may not be expressed as (each term has its usual meaning)

x=Asin(ωt+ϕ)

x=Acos(ωt−ϕ)

x=asinωt+bcosωt

x=Asin(ωt+ϕ)+Bsin(2ωt+ϕ)

The fourth option is a superposition of two S.H.M.'s will different frequencies and time periods. Hence it is not a true S.H.M

$x = A sin (ω t + ϕ)$

$x = A cos (ω t - ϕ)$

$x = a sin ω t + b cos ω t$

$x = A sin (ω t + ϕ) + B sin (2 ω t + ϕ)$