Question

Out of the following functions representing motion of particle which represents SHM?
1. $x=si{n}^3\omega t$
2. $x=1+\omega t+{\omega }^2{t}^2$
3. $x=cos\omega t+cos3\omega t+cos5\omega t$
4. $x=sin\omega t+cos\omega t$

• A. Only 1
• B. Only 1 and 3
• C. Only 1 and 4
• D. Only 4

Answer 1

The correct option is D Only 4

For SHM of a particle :

$a\propto -x$

$x=sin\omega t+cos\omega t$

$v=\frac{dx}{dt}=\omega (cos\omega t-sin\omega t)$

Again

$a=\frac{dv}{dt}=-{\omega }^2(sin\omega t+cos\omega t)$

Hence, $a=-x$

After differentiating other equation, SHM condition will not satisfy,

Option D