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?
A) $x = a\sin{bt}$
B) $x = a\cos{bt + c}$
C) $x = a\sin{bt + c\cos{bt}}$
D) $x = a\sec{bt + c\ cosec\ bt}$
Explanation
(d) $Sec\ bt$ is not defined for $bt = \pi/2$
$x = a\sec{bt} + c\ cosec\ bt = \frac{a\sin{bt} + c\cos{bt}}{\sin{bt\cos{bt}}}$
This equation cannot be modified in the form of simple equation of SHM $ie$,
$x = a\sin{(\omega t + \phi)}$
So, it cannot represent SHM
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.