### Q.9:- 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:-**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:

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

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

*a* = ω^{2} *A*

where,

Hence, the maximum acceleration of the mass is 8.0 m/s^{2}.

(iii) Maximum velocity, *v*_{max} = *A*ω

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