Question

Which of the following expressions represents an oscillatory motion ?

• A. $F=-2(x-2{)}^2$
• B. $F=2(x-2{)}^3$
• C. $F=2(x-2{)}^2$
• D. $F=-2(x-2{)}^3$

Answer 1

The correct option is D $F=-2(x-2{)}^3$

Any oscillatory motion can be represented by
$F=-k(x-a{)}^n$
where, $n$ is an odd number and $x=a$ is mean position.
So, $F=-2(x-2{)}^3$ is an oscillatory motion, with mean point at $x=2$

Note $\to$ For the oscillatory motion to be S.H.M, $n=1$