Question

The differential equation of displacement of all "Simple harmonic motions" of given period $2 \pi / n$, is

• A. $\frac { d ^ { 2 } x } { d t ^ { 2 } } + n x = 0$
• B. $\frac { d ^ { 2 } x } { d t ^ { 2 } } + n ^ { 2 } x = 0$
• C. $\frac { d ^ { 2 } x } { d t ^ { 2 } } - n ^ { 2 } x = 0$
• D. $\frac { d ^ { 2 } x } { d t ^ { 2 } } + \frac { 1 } { n ^ { 2 } } x = 0$

Answer 1

Answer: (B)

$\frac { d ^ { 2 } x } { d t ^ { 2 } } + n ^ { 2 } x = 0$

Answer 2

The displacement of x for all S.H.M. is given by

$x = a \cos ( n t + b )$ ⇒$\frac { d x } { d t } = - n a \sin ( n t + b )$

⇒ $\frac { d ^ { 2 } x } { d t ^ { 2 } } = - n ^ { 2 } a \cos ( n t + b )$ ⇒ $\frac { d ^ { 2 } x } { d t ^ { 2 } } = - n ^ { 2 } x$

⇒ $\frac { d ^ { 2 } x } { d t ^ { 2 } } + n ^ { 2 } x = 0$.