Question

Which one of the following equations of motion represents simple harmonic motion?
where $k, k_{0}, k_{1}$ and $a$ are all positive.

• A. Acceleration $= - k (x + a)$
• B. Acceleration $= k (x + a )$
• C. Acceleration $= kx$
• D. Acceleration = - $ k_0 x + k_1 x^2 $

Answer 1

Answer: (A)

equation of S.H.M
$a =-\frac{d^{2} x}{d t^{2}}=-w^{2} x$
$w =\sqrt{\frac{k}{m}}$
where in,
$x=A \sin (w t+\delta) $
$a=-k x$
where, $x=x+a$
$a=-k(x+a)$