Two light spring of force constants `k_(1) and k_(2)` and a block of mass m are in the line AB on a smooth horizontal table such that one end of each spring is fixed on right supports and the other and is free as shown in figure
The distance CD between the free ends of the spring is `60 cm`. If the block moves with a velocity of 120cm/s between C and D and `(k_(1) = 1.8 N//m, k_(2) = 3.2 N//m and m = 200g)`. Is the motion simple harmonic?
Two light spring of force constants `k_(1) and k_(2)` and a block of mass m are in the line AB on a smooth horizontal table such that one end of each spring is fixed on right supports and the other and is free as shown in figure
The distance CD between the free ends of the spring is `60 cm`. If the block moves with a velocity of 120cm/s between C and D and `(k_(1) = 1.8 N//m, k_(2) = 3.2 N//m and m = 200g)`. Is the motion simple harmonic?
The distance CD between the free ends of the spring is `60 cm`. If the block moves with a velocity of 120cm/s between C and D and `(k_(1) = 1.8 N//m, k_(2) = 3.2 N//m and m = 200g)`. Is the motion simple harmonic?
A
`1.04 sec`
B
`0.785 sec`
C
`1sec`
D
`2.82sec`
Text Solution
Verified by Experts
The correct Answer is:
D
`t = t_(1) +t_(2) +t_(3)`, let `C',D'` be the exterme positions of the springs `k_(2),k_(1)` respectively.
`t_(1) = t_(DL) +t_(D'D) = (T_(1))/(2) = pi sqrt((m)/(k_(1)))`
`:. T_(2) = t_(DC) +t_(CD) = (2L)/(v), t_(3) = t_(C C') +t_(C' C) = (T_(2))/(2) = pi sqrt((m)/(k_(2)))`
`t_(1) = t_(DL) +t_(D'D) = (T_(1))/(2) = pi sqrt((m)/(k_(1)))`
`:. T_(2) = t_(DC) +t_(CD) = (2L)/(v), t_(3) = t_(C C') +t_(C' C) = (T_(2))/(2) = pi sqrt((m)/(k_(2)))`
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Knowledge Check
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A
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B
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D
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