First slide

Simple hormonic motion

Question

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

Easy

A

$\large b{x^2}$
B

$\large a + bx - c{x^2}$
C

–bx
D

$\large a - bx + c{x^2}$

Solution

Condition for S.H.M is
acceleration $\large \propto$ [– displacement]
F = -bx
$\large \Rightarrow$ ma = -bx
$\large \Rightarrow$ $\large a\, = \, - \left( {\frac{b}{m}} \right)x$
$\large \therefore \,a\, \propto \,\left( { - x} \right)$

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