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Three springs are connected to a mass m=...

Three springs are connected to a mass `m= 80 g` as shown in figure. What is the effective spring constant and periodic time, if `k= 2 Nm^(-1)`?

Text Solution

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Here, `k= 2 Nm^(-1), m= 80g = 80xx 10^(-3) kg = 0.08 kg`
Here all the three spring are in parallel so eaquivalent force constant,
`k. = 2k+ k+k = 4k`
Periodic time `T = 2pi sqrt((m)/(k.))`
`=2pi sqrt((0.08)/(4k)) = 2pi sqrt((0.08)/(4xx2))`
`= 2pi xx sqrt(0.01) = 2 xx 3.14 xx 0.1`
`therefore T = 0.628s`.
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