(^534) A Textbook of Engineering Mechanics
(b) When the springs are connected in parallel
We know that spring constant of an equivalent spring,
s = s 1 + s 2 = 4 + 6 = 10 kN /m
and deflection of the spring due to block of weight 0·49 kN
0.05 9.8
0·049 m
10
×
δ= =
∴ Period of vibrations
0·049
22 =0.44s
9·8
t
g
δ
=π =π× Ans.
We know that angular velocity of the block,
22
14·28 rad/s
t 0·44
ππ
ω= = =
∴ Maximum velocity, vmax = ωr = 14·28 × 0·04 = 0·57 m/s Ans.
and maximum acceleration, = ω^2 r = (14·28)^2 × 0·04 = 8·16 m/s^2 Ans.
Example 26.7. A weight P is attached to springs of stiffness C 1 and C 2 in two different cases
as shown in Fig. 26.4.
Fig. 26.4.
Determine the period of vibrations in both the cases.
Solution. Given : Weight = P
Period of vibrations in the first case
We know that in this case both the springs will be subjected to the weight P. Therefore total
displacement of the spring
12
12 12 12
PP 11 PC()C
P
CC CC CC
⎛⎞+
=+ =⎜⎟+ =
⎝⎠
and period of vibration 12
12
Displacement ()
22
Acceleration
PC C
gC C
- =π =π Ans.
Period of vibrations in the second case
We know that in this case, the upper spring will be subjected to tension, whereas the lower
one will be subjected to compression.