Question

An object performing S.H.M. with mass of 0.5 kg, force constant 10N/m and amplitude 3cm, What are kinetic and potently energies when x = 2 cm?
(Ans : K.E. = 0.00251, P.E. = 0.002J)

Answer 1

kinetic energy of an object performing S.H.M at x distance from mean position is given by $K.E=\frac{1}{2}\kappa(A^2-x^2)$

here, $\kappa=10N/m$
x = 2cm , A = 3cm

so, K.E = 1/2 × 10 × (0.03² - 0.02²)

K.E = 1/2 × 10 × (0.0009 - 0.0004)

K.E = 1/2 × 10 × 0.0005

K.E = 0.0025J

potential energy of an object performing S.H.M at x distance from mean position is given by $P.E=\frac{1}{2}\kappa x^2$

P.E = 1/2 × 10 × (0.02)²

P.E = 1/2 × 10 × 0.0004

P.E = 0.002J