A spring having with a spring constant is mounted on a horizontal table as shown in Fig. 14.24. A mass of is attached to the free end of the spring. The mass is then pulled sideways to a distance of and released.

Determine<br>(i) the frequency of oscillations,

(ii) maximum acceleration of the mass

Solution:

Spring constant is given as

Mass is given as
Displacement is given as

(i) Frequency of oscillation ‘ ‘ can be calculated as,

Where,
time period

So,

As a result, the frequency of oscillations is cycles per second.

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

Where,

Maximum displacement

So,

As a result, the maximum acceleration of the mass is