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An oscillating block- spring system has ...

An oscillating block- spring system has a mechanical energy of 1.00 J , an amplitude of 10.0 cm and a maximum speeding of `1.20 m//s` . Find the spring constant, the mass of the block, and the frequency of oscillation

Text Solution

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`E=1.00J,A=10.0cm = 0.10m, v_(m)=1.20m//s`
k = ? , m = ? , f = ?
The total mechanical energy of a block spring system is related at A and `v_(m)`
`E=1/2mv_(m)^(2)` (occurs when x = 0 so P.E = 0 )
`E=1/2kA^(2)` (occurs when v = 0 so K.E = 0 )
`E=1/2kA^(2)impliesk=(2E)/(A^(2))=(2(1.00J))/((0.10)^(2))implies200Nm^(-1)`
`E=1/2mv_(m)^(2)impliesm=(2E)/(V_(m)^(2))=(2(1.00J))/((0.10))impliesm=1.39kg`
`f=1/(2pi)sqrt((k)/(m))=1/(2pi)sqrt((200)/(1.39))impliesf=1.90Hz.`
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