Question

An object performing S.H.M. with mass of 0.5 kg, force constant 10N/m and amplitude 3cm, What is its maximum speed?
(Ans : Vmax = 0.1342 m/s )

Answer 1

we know, kinetic energy of object performing S.H.M at mean position is given by $K.E=\frac{1}{2}\kappa A^2$
actually, maximum speed can be found at mean position. so, we have to take formula of kinetic energy of object at mean position.

but we know, kinetic energy $K.E=\frac{1}{2}mv^2$

$\frac{1}{2}mv^2=\frac{1}{2}\kappa A^2$

$mv^2=\kappa A^2$

given, m = 0.5 kg
$\kappa=10N/m$
$A=3cm=3\times10^{-2}m$

0.5 × v² = 10 × (3 × 10^-2)²

v² = 20 × 9 × 10^-4

v² = 0.0180

v = 0.134164079 m/s