Which of the following expressions does not represent simple harmonic motion?

Question

Which of the following expressions does not represent simple harmonic motion? (A) x=A cos ω t +B sin ω t (B) x=A cos (ω t+α) (C) x=B sin (ω t+β) (D) x=A sin ω t cos2ω t

Tardigrade Admin · Accepted Answer

Simple harmonic motion is represented by a sine function or a cosine function or a linear combination of both. Hence, options (a), (b) and (c) represent simple harmonic motion while option (d) is a product of the two functions (sine and cosine) does not represent a simple harmonic motion.

Q. Which of the following expressions does not represent simple harmonic motion?

$x = A cos ω t + B s inω t$

$x = A cos (ω t + α)$

$x = B s in (ω t + β)$

$x = A s inω t co s^{2} ω t$

Simple harmonic motion is represented by a sine function or a cosine function or a linear combination of both. Hence, options $(a), (b)$ and $(c)$ represent simple harmonic motion while option $(d)$ is a product of the two functions (sine and cosine) does not represent a simple harmonic motion.

Q. Which of the following expressions does not represent simple harmonic motion?

x=Acosωt+Bsinωt

x=Acos(ωt+α)

x=Bsin(ωt+β)

x=Asinωtcos2ωt

Simple harmonic motion is represented by a sine function or a cosine function or a linear combination of both. Hence, options (a),(b) and (c) represent simple harmonic motion while option (d) is a product of the two functions (sine and cosine) does not represent a simple harmonic motion.

$x = A cos ω t + B s inω t$

$x = A cos (ω t + α)$

$x = B s in (ω t + β)$

$x = A s inω t co s^{2} ω t$

Simple harmonic motion is represented by a sine function or a cosine function or a linear combination of both. Hence, options $(a), (b)$ and $(c)$ represent simple harmonic motion while option $(d)$ is a product of the two functions (sine and cosine) does not represent a simple harmonic motion.