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A spring is suspended under gravity with a block attached to i

Question

A spring is suspended under gravity with a block attached to it. The block oscillates in the vertical plane according to $x = a s in wt$ with time period $8$ seconds. The ratio of velocities of the particle at $t = 1$ sec to $t = 3$ sec is

2 : 1

1 : 1

3 : 4

2 : 3

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A spring is suspended under gravity with a block attached to it. The block oscillates in the vertical plane according to

x = a s in wt

with time period

8

seconds. The ratio of velocities of the particle at

t = 1

sec to

t = 3

sec is

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Text solutionVerified

x = a s inω t

V = \frac{d x}{x t} = aω cos ω t

T = \frac{2 π}{ω}; ω = \frac{2 π}{T} = \frac{π}{4} \frac{r a d}{sec}

\frac{V _{1}}{V _{2}} = \frac{cos ω t _{1}}{cos ω t _{2}} = \frac{cos \frac{π}{4}}{cos \frac{3 π}{4}} = \frac{1}{1}

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Question Text	A spring is suspended under gravity with a block attached to it. The block oscillates in the vertical plane according to $x = a s in wt$ with time period $8$ seconds. The ratio of velocities of the particle at $t = 1$ sec to $t = 3$ sec is
Answer Type	Text solution:1
Upvotes	150