A 0.50-kg mass is suspended from a massless spring that has a force constant of 79 N/m. The mass is displaced 0.1 m down from its equilibrium position and released. If the downward direction is negative, the displacement of the mass as a function of time is given by
A) y = 0.1 cos158t - $\pi$)
B) y = 0.2 cos158t - $\pi$)
C) y = 0.1 cos12.6t - $\pi$)
D) y = 0.2 cos12.6t + $\pi$)
E) y = 0.1 cos2t + $\pi$)

Question

A 0.50-kg mass is suspended from a massless spring that has a force constant of 79 N/m. The mass is displaced 0.1 m down from its equilibrium position and released. If the downward direction is negative, the displacement of the mass as a function of time is given by
A) y = 0.1 cos158t -  $\pi$)
B) y = 0.2 cos158t -  $\pi$)
C) y = 0.1 cos12.6t -  $\pi$)
D) y = 0.2 cos12.6t +  $\pi$)
E) y = 0.1 cos2t +  $\pi$)

Quizplus · Accepted Answer

The equation for the displacement of a mass on a spring is given by:
$$y = A \cos(\omega t)$$
where A is the amplitude of the oscillation and $\omega$ is the angular frequency, given by:
$$\omega = \sqrt{\frac{k}{m}}$$
where k is the force constant of the spring and m is the mass on the spring.

Plugging in the given values, we get:
$$\omega = \sqrt{\frac{79 N/m}{0.50 kg}} = \sqrt{158} rad/s$$

At t = 0, the displacement is 0.1 m, thus the amplitude is 0.1 m.

The displacement equation is then:
$$y = 0.1 \cos(12.6t)$$

Therefore, the best choice is (C).

A 050-Kg Mass Is Suspended from a Massless Spring That Has