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Four massless spring whose force constan...

Four massless spring whose force constant are `2k , 2k, k` and `2k` respectively are attached to a mass `M` kept on a frictions plate (as shown in figure) if the mass `M` is displaced in the horizontal direction then the frequency of oscillation of the system is

A

`(1)/(2pi) sqrt((k)/(4M))`

B

`(1)/(2pi) sqrt((4k)/(M))`

C

`(1)/(2pi) sqrt((k)/(7M))`

D

`(1)/(2pi) sqrt((7k)/(M))`

Text Solution

Verified by Experts

The correct Answer is:
B
The spring on left side having spring constant of `2k` each are in saries equvalent constant is `(1)/(((1)/(2k) + (1)/(2k))) = k`. The two spring on right hand side of mass `M` are in parallel Their effective spring constant is `(k + 2k) = 3k`.
Equivalent spring constant of value `k` and `3k` are in parallel and their and their net value of spring constant of all the four spring is `k + 3k = 4k`
:. Frequency of mass is `n = (1)/(2pi) sqrt((4k)/(M))`.
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Knowledge Check

  • Four massless springs whose force constants are 2k, 2k, k and 2k respectively are attached to a mass M kept on a frictionless plane (as shown in figure). If the mass M is displaced in the horizontal direction.

    A
    `(1)/(2pi)sqrt((k)/(4M))`
    B
    `1/(2pi)sqrt((4k)/M)`
    C
    `1/(2pi)sqrt(k/(7M)`
    D
    `1/(2pi)sqrt((7k)/M)`

  • Four massless springs whose force constants are 2k,2k, k and 2k, respectively, are attached to a mass M kept on a frictionless plane (as shown in figure), If the mass M is displaced in the horizontal direction, then the frequency of oscillation of the system is

    A
    `(1)/(2pi)sqrt(k/(4M)`
    B
    `(1)/(2pi)sqrt((4k)/(M)`
    C
    `(1)/(2pi)sqrt((k)/(7M)`
    D
    `(1)/(2pi)sqrt((7k)/(M)`

  • Four massless springs whose force constants are 2k, 2k, k and 2k respectively are attached to a mass M kept on a fricaionless plane (as shown in figure). If the mass M is displaced in the horizontal directions, then the frequency of the system.

    A
    `(1)/(2pi)sqrt((k)/(M))`
    B
    `(1)/(2pi)sqrt((4k)/(M))`
    C
    `(1)/(2pi)sqrt((k)/(7M))`
    D
    `(1)/(2pi)sqrt((7k)/(M))`

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