A force of 6.4, N stretches a vertical spring by 0.1 ,m . mass that must be suspended from spring so

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13.Oscillations

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A force of $6.4\, N$ stretches a vertical spring by $0.1 \,m$. The mass that must be suspended from the spring so that it oscillates with a period of $\left( {\frac{\pi }{4}} \right)sec$. is ... $kg$

A

$\left( {\frac{\pi }{4}} \right)$

B

$1$

C

$\left( {\frac{1}{\pi }} \right)$

D

$10$

Solution

(b) Force constant of a spring is given by $F = kx$

$6.4 = k(0.1)$ or $k = 64N/m$

$T = 2\pi \sqrt {\frac{m}{k}} $ ==> $\frac{\pi }{4} = 2\pi \sqrt {\frac{m}{{64}}} $; $\frac{m}{{64}} = {\left( {\frac{1}{8}} \right)^2}$; $m = 1kg$

Standard 11

Physics

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