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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 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?

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)))`
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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 (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 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 )

Knowledge Check

  • A block of mass m moving with velocity v_(0) on a smooth horizontal surface hits the spring of constant k as shown. Two maximum compression in spring is

    A
    `sqrt((2m)/(k))v_(0)`
    B
    `sqrt((m)/(k)).v_(0)`
    C
    `sqrt((m)/(k)).v_(0)`
    D
    `(m)/(2k).v_(0)`

  • A block of mass m, attacted to a string of spring constant k, oscillates on a smooth horizontal table. The other end of the spring is fixed to a wall. The block has a speed v when the spring is at its natural length. Before coming to an instantaneous rest. If the block moves a distance x from the mean position, then

    A
    `x=sqrt((m)/(k))`
    B
    `a=(1)/(v)sqrt((m)/(k))`
    C
    `x=v sqrt((m)/(k))`
    D
    `x=sqrt((mv)/(k))`

  • As shown in the figure, two light springs of force constant k_(1) and k_(2) oscillate a block of mass m. Its effective force constant will be

    A
    `k_(1)k_(2)`
    B
    `k_(1)+k_(2)`
    C
    `(1)/(k_(1)) +(1)/(k_(2))`
    D
    `(k_(1)k_(2))/(k_(1)+k_(2))`

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