Question

When a small mass of 120g is attached to a vertical spring, the spring stretches by 8.00cm where the small mass hangs at rest. The mass is then pulled down 3.00cm from its rest position and released so that the mass oscillates up and down. What maximum speed does the mass have during its oscillation?

ANS: 33.2 cm/s

Answer 1

Gravitational acceleration = g = 9.81 m/s²

Mass of the object = m = 120 g = 0.12 kg

Spring constant = k

Amount the spring stretches due to the weight of the object = X = 8 cm = 0.08 m

mg = kX

(0.12)(9.81) = k(0.08)

k = 14.715 N/m

The mass is pulled down by 3 cm and the mass then oscillates.

Amplitude of oscillation = A = 3 cm

Angular frequency of oscillation =

= 11.07 rad/s

Maximum speed of the mass during it's oscillation = V

V = A

V = (3)(11.07)

V = 33.2 cm/s

Maximum speed of the mass during it's oscillations = 33.2 cm/s