IIT JEE , AIEEE Forum - Physics , Mechanics

waterdemon

Note:
Spring B = Y axis
Spring A = X axis
Spring C = Z axis (making angle 45 with x axis.)

Let "x" be the displacement of SpringC.

The displacement of A = (x)Cos(45) = x/

2

Similarly,The displacement of B
=xSin(45)
=x/

2

Now the forces acting on "m" in the displaced position of m
are:

Kx in the direction of Spring C.
Kx/

2 in the direction of Spring B
Kx/

2 in the direction of Spring A

Therefore the Net Force in the direction of Spring C

=Kx +

[(Kx/

2)² + (Kx/

2)²]
=2Kx.

Therefore,
m(d²x/dt²) = 2Kx

(d²x/dt²) = (2K/m)x

= 2

/T

=

K/M

Therefore,

T = 2

(m/2K)

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