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Two light spring of force constants k(1)...

Two light spring of force constants `k_(1)` and `k_(2)` and a block of mass m are in one line `AB` on a smooth horizontal table such that one end of each spring is fixed on rigid supports and the other end is free as shown in the figure. The distance `CD` between the spring is `60cm`. If the block moves along `AB` with a velocity `120 cm//s` in between the springs, calculate the period of oscillation of the block. (take `k_(1) = 1.8 N//m`, `k_(2) = 3.2 N//m`, `m = 200 g`)

Text Solution

Verified by Experts

The correct Answer is:
`2.82 s`
Between `C` and `D` block will move with constant speed of `120 cm//s`. Therefore, period of oscillation will be (starting from `C`).
`T = t_(CD) + (T_(2))/(2) + t_(DC) + (T_(1))/(2)`
Here, `T_(1) = 2pisqrt((m)/(k_(1))` and `T_(2) = 2pisqrt((m)/(k_(2))`
and `t_(CD) = T_(DC) = (CD)/(v) = (60)/(120) = 0.5 s`
`:. T = 0.5 + (2pi)/(2)sqrt((0.2)/(3.2)) + 0.5 + (2pi)/(2)sqrt((0.2)/(1.8))`
`(m = 200 g = 0.2 kg)`
`T = 2.82 s`
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