(^530) „„„„„ A Textbook of Engineering Mechanics
We know that periodic time,
11
0.5 s
2
t
n

We also know that periodic time,
4
0.5 2 2
m
ss
=π =π
Squaring both sides,
0.25 (2 )^2 4157.9
ss
=π× =
157.9
631.6 N/m
0.25
s== Ans.
Example 26.2. A spiral spring hung up at one end, and carrying a mass of 7 kg at the
other is made to vibrate. Find the period of oscillation, if the spring is found to extend 10 mm
for each 0.5 kg of mass.
Solution. Given : Mass = 7kg and when mass = 0.5 kg, then deflection (δ) = 10 mm = 0.01 m.
We know that when mass is equal to 7 kg, then deflection of the spring
0.01
70.14m
0.5
δ= × =
and period of oscillation,
0·14
22 0·75s
9·8
t
g
δ
=π =π = Ans.
Example 26.3. A mass supported by a spring has a static deflection of 0.5 mm. Determine
its natural frequency of oscillation.
Solution. Given: Deflection (δ) = 0.5 mm = 0.0005 m
We know that natural frequency of oscillation,
119·8
2 2 0·0005
g
n==
πδ π
= 22·3 vib/s = 22·3 Hz Ans.
Example 26.4. A body of mass 3 kg, suspended from a vertically mounted spring, deflects it
by 12 mm. Determine the no. of oscillations of the body.
Also determine the maximum force in the spring, when it is displaced through a distance of
25 mm from its rest position and then released.
Solution. Given : Mass of the body (m) = 3 kg ; Deflection (δ) = 12 mm = 0.012 m and
displacement (x) = 25 mm = 0.025 m
No. of oscillations of the body
We know that the no. of oscillations of the body,
119·8
2 2 0.012
g
n==
πδ π
= 4·55 vib/s = 4·55 Hz Ans.