A 0.30kg mass hangs at rest from a light vertical spring of force constant 50N/m. First, the mass is displaced vertically and released so that it oscillates along the spring’s axis. Later, the mass is returned to equilibrium, pulled sideways a small distance, and released so that it swings like a pendulum while the spring remains nearly vertical and unchanged in length. Which statement correctly compares the periods of the two resulting small-amplitude motions?
(a) The two periods are equal because both motions are simple harmonic.
(b) The sideways swing has the longer period, since a pendulum of the spring’s equilibrium length oscillates more slowly than a mass–spring system with the same m and k.
(c) The vertical oscillation has the longer period because its period increases with the mass, whereas the pendulum’s period does not depend on mass.
(d) The periods cannot be compared without knowing the spring’s unstretched length, which determines the pendulum length.