Question

Un resorte se monta horizontalmente con su extremo izquierdo fijo. Conectando una balanza de
resorte al extremo libre y tirando hacia la derecha, determinamos que la fuerza de estiramiento es
proporcional al desplazamiento y que una fuerza de 6 N causa un desplazamiento de 0,03m.
quitamos la balanza y conectamos un cuerpo 0,5 kg al extremo, tiramos de èl hasta moverlo 0,02 m,
lo soltamos y vemos como oscila. Determine la constante del resorte. Calcule la velocidad angular, la
frecuencia y el período de oscilación

1. Jezebel

Translation of important question part (Google translation used)

Force of 6N causes a displacement of 0.03m. remove the balance and connect a body 0.5 kg to the end, pull it to move it 0.02 m, release it and see how it oscillates.

(a)Determine the spring constant.

(b)Calculate angular velocity, frequency, and oscillation period

(a)K=200 N/m

(b) w= 20 rad/s f=3.2 Hz T=0.3125 s

Explanation:

(a)

From Hooke’s law, we deduce that F=kx where F is applied force, k is spring constant and x is extension of the spring. Making k the subject of the formula then k=F/x and substituting F with 6 N and x with 0.03 m then k=6/0.03=200 N/m

(b)

Angular velocity, w is given by where m is the mass and k is spring constant calculated in part a above. Substituting mass with 0.5 kg and k with 200 N/m then

We know that frequency, f is given by and substituting 20 rad/s for w then

Finally, oscillation period, T is usually the reciprocal of frequency hence T=1/f and substituting f with 3.2 Hz then T=1/3.2=0.3125 s