Question

A spring having with a spring constant 1200 N m^–1 is mounted on a horizontal table as shown in Fig. A mass of 3 kg is attached to the free end of the spring. The mass is then pulled sideways to a distance of 2.0 cm and released.

Determine (i) the frequency of oscillations, (ii) maximum acceleration of the mass, and (iii) the maximum speed of the mass.

Answer 1

Spring constant, k = 1200 N m^–1

Mass, m = 3 kg

Displacement, A = 2.0 cm = 0.02 cm

(i) Frequency of oscillation v, is given by the relation:

Where, T is the time period

Hence, the frequency of oscillations is 3.18 cycles per second.

(ii) Maximum acceleration (a) is given by the relation:

a = ω² A

Where,

ω = Angular frequency =

A = Maximum displacement

Hence, the maximum acceleration of the mass is 8.0 m/s².

(iii) Maximum velocity, v_max = Aω

Hence, the maximum velocity of the mass is 0.4 m/s.