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

Answer 1

Answer: (D)

As, sec $b t$ is not define for $b t=\pi / 2$
and $x=a \sec \,bt + c \,cosec \,bt=\frac{a \sin\, b t+c \,\cos \,b t}{\sin \,b t \cos\, b t}$
This equation cannot be modified in the form of simple equation of $SHM$ i.e.,
$x=a \sin (\omega t+\phi)$
So, it cannot represent SHM