Question

Which of the following expressions represents an oscillatory motion ?

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

Answer 1

Answer: (A), (C)

The correct options are
A $F=-2(x-2{)}^3$
C $F=-2x^3$

Any oscillatory motion can be represented by
$F=-k(x-a{)}^n$
where, $n$ is an odd number and $x=a$ is the mean position.
So, $F=-2(x-2{)}^3$ is an oscillatory motion with mean point at $x=2$.
and $F=-2x^3$ is an oscillatory motion with mean point at $x=0$.

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