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Two light springs of force constants (k1...

Two light springs 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 free ends of the springs is (60 cms). If the block moves along (AB) with a velocity (120 cm//sec) in between the springs, calculate the period of oscillation of the block `k_1 = 1.8 N//m, k_2 = 3.2 N//m, m = 200 gm)`.
(##JMA_CHMO_C10_026_Q01##).

Text Solution

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The correct Answer is:
B
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) = 2pi sqrt((m)/(k_(1)))` and `T_(2) = 2pi sqrt((m)/(k_(2))`
and `t_(CD) = t_(DC) = (60)/(120) = 0.5s`
`:. T = 0.5 + (2pi)/(2)sqrt((0.2)/(3.2)) + 0.5 + (2pi)/(2)sqrt((0.2)/(1.8))`
`T = 2.82 s`
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