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Dahasolnce [82]

3 years ago

10

A 0.415-kg mass suspended from a spring undergoes simpleharmonic oscillations with a period of 1.4 s. How much mass, inkilograms

, must be added to the object to change the period to2.2 s?

1 answer:

koban [17]3 years ago

6 0

Answer:

m=0.893kg

Explanation:

time period of oscillations is given by= 2π√(m/k)

m: mass of the object

k: spring constant

when T=1.5 and m=0.415

1.5= 2π√(0.415/k)

k= 7.27 N/m

when T= 2.2s

2.2= 2π√(m/7.27)

m=0.893kg

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$A=\dfrac{\dfrac{0.5}{0.254}}{\sqrt{(10.0^2-3.14)^2+0.628^2\times3.14^2}}$

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$tan d=\dfrac{0.628\times3.14}{((10.0^2-3.14)^2)}$

$d=0.0120$

Put the value of $\omega=6.28\ rad/s$ in equation (I) and (II)

$A=\dfrac{\dfrac{0.5}{0.254}}{\sqrt{(10.0^2-6.28)^2+0.628^2\times6.28^2}}$

$A=0.0209$

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$tan d=\dfrac{0.628\times6.28}{((10.0^2-6.28)^2)}$

$d=0.0257$

Put the value of $\omega=9.42\ rad/s$ in equation (I) and (II)

$A=\dfrac{\dfrac{0.5}{0.254}}{\sqrt{(10.0^2-9.42)^2+0.628^2\times9.42^2}}$

$A=0.0217$

From equation (II)

$tan d=\dfrac{0.628\times9.42}{((10.0^2-9.42)^2)}$

$d=0.0413$

Hence, This is the required solution.

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