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A block of unknown mass is attached to a spring with a spring constant of 10 N/m and...
A block of unknown mass is attached to a spring with a spring constant of 10 N/m and undergoes simple harmonic motion with an amplitude of 8.0 cm. When the block is 1/4 of the way between its equilibrium position and the endpoint, its speed is measured to be 30.0 cm/s. Calculate the mass of the block and period.
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To solve this problem, the knowledge of the Hooke’s law is necessary.
Spring constant (k) = 10 N/m
amplitude = x(max) = 8.0 cm = 0.08 m
speed (v) = 30.0cm/s 0.3 m/s
1. Calculate the mass of the block
`omega = (v)/(x_(max)) = sqrt(k/m)`
`omega = (0.3)/(0.08) = sqrt(10/m)`
`omega = 3.75 = sqrt(10/m)`
`(3.75 = sqrt(10/m))^(2)`
`3.75^(2) = 10/m`
`m = 10/(3.75^(2))`
`m = 0.71 kg`
2. Calculate the period, T
`omega = (2 pi)/T`
`3.75 = (2 pi)/T`
`T = (2 pi)/3.75`
`T = 1.68 s`
Posted by jerichorayel on May 30, 2013 at 3:39 PM (Answer #1)
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