Which of the following expressions corresponds to simple harmonic motion along a straight line, where x is the displacement and a, b, c are positive constants ?

Question

Which of the following expressions corresponds to simple harmonic motion along a straight line, where x is the displacement and a, b, c are positive constants ? (A) a + bx - cx2 (B) bx2 (C) a - bx + cx2 (D) - bx

Tardigrade Admin · Accepted Answer

In linear S.H.M., the restoring force acting on particle should always be proportional to the displacement of the particle and directed towards the equilibrium position.

i.e.,

F \propto x

or

F = - b x

where

b

is a positive constant.

Q. Which of the following expressions corresponds to simple harmonic motion along a straight line, where $x$ is the displacement and $a, b, c$ are positive constants ?

$a + b x - c x^{2}$

$b x^{2}$

$a - b x + c x^{2}$

$- b x$

In linear S.H.M., the restoring force acting on particle should always be proportional to the displacement of the particle and directed towards the equilibrium position.

i.e., $F \propto x$
or $F = - b x$ where $b$ is a positive constant.

Q. Which of the following expressions corresponds to simple harmonic motion along a straight line, where x is the displacement and a,b,c are positive constants ?

a+bx−cx2

bx2

a−bx+cx2

−bx