Question

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 slightly in the horizontal direction, then the frequency of oscillation of the system is,

• A.
• B.
• C.
• D.

Answer 1

The correct option is B

Springs on the left of the block are in series, hence their equivalent spring constant is

$K_1=\frac{\left(2K\right)\left(2K\right)}{2K+2K}=K$

Spring on the right of the block are in parallel, hence their equivalent spring constant is

$K_2=K+2K=3K$

Again both $K_1$ and $K_2$ are in parallel

$\therefore K_{eq}=K_1+K_2=K+3K=4K$

Hence, frequency is $f=\frac{1}{2\pi }\sqrt{\frac{K_{eq}}{M}}=\frac{1}{2\pi }\sqrt{\frac{4K}{M}}$