Which one of the following equations does not represent SHM, x= displacement and t= time. Parameters a, b and c are the constants of motion?

Question

Which one of the following equations does not represent SHM, x= displacement and t= time. Parameters a, b and c are the constants of motion? (A) x = a sin b t (B) x = a cos b t + c (C) x = a sin bt + c cos bt (D) x = a sec b t + c cosec b t

Tardigrade Admin · Accepted Answer

As, sec b t is not define for b t=π / 2 and x=a sec bt + c cosec bt=(a sin b t+c cos b t/ sin b t cos b t) This equation cannot be modified in the form of simple equation of SHM i.e., x=a sin (ω t+φ) So, it cannot represent SHM

Q. Which one of the following equations does not represent SHM, $x =$ displacement and $t =$ time. Parameters $a, b$ and $c$ are the constants of motion?

x = a sin b t

x = a cos b t + c

x = a sin bt + c cos bt

x = a sec b t + c cosec b t

As, sec $b t$ is not define for $b t = π /2$
and $x = a sec b t + c cosec b t = \frac{a s i n b t + c c o s b t}{s i n b t c o s b t}$
This equation cannot be modified in the form of simple equation of $S H M$ i.e.,
$x = a sin (ω t + ϕ)$
So, it cannot represent SHM

Q. Which one of the following equations does not represent SHM, x= displacement and t= time. Parameters a,b and c are the constants of motion?