Answer:
(a) Here, M = 3000 kg ; x = \[\text{T=2 }\!\!\pi\!\!\text{
}\sqrt{\frac{\text{inertia factor}}{\text{spring factor}}}\] m ; If k is the
spring constant of each spring, then spring constant of 4 springs in parallel
to support the whole mass is, K = 4 k
\[\text{=2 }\!\!\pi\!\!\text{
}\sqrt{\frac{\text{m}}{\text{E}{{\text{A}}^{\text{2}}}\text{/V}}}\text{=}\frac{\text{2
}\!\!\pi\!\!\text{ }}{\text{A}}\sqrt{\frac{\text{mV}}{\text{E}}}\] 4 kx = mg
or \[\therefore \]
\[\text{v=}\frac{\text{1}}{\text{T}}\text{=}\frac{\text{A}}{\text{2
}\!\!\pi\!\!\text{ }}\sqrt{\frac{\text{E}}{\text{mV}}}\]
(b)
If m is the mass supported by each spring, then \[E=\gamma P,\]
From
\[\text{ }\!\!\gamma\!\!\text{
=}{{\text{C}}_{\text{p}}}\text{/}{{\text{C}}_{\text{ }\!\!\upsilon\!\!\text{
}}}\text{.}\]\[\text{m/}{{\text{s}}^{\text{2}}}\]or \[0\cdot 15\]
or
\[\therefore \]
or
\[k=\frac{Mg}{4x}\]
Now,
\[=\frac{3000\times 10}{4\times 0\cdot 15}=5\times {{10}^{4}}N/m\]
From
(i)
\[m=\frac{3000}{4}=750kg\]
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