Question

Two springs, each of spring constant k, are attached to a block of mass m as shown in the figure. The block can slide smoothly along a horizontal platform clamped to the opposite walls of the trolley of mass M. If the block is displaced by x cm and released, the period of oscillations is :

• A. $T=2\pi \sqrt{\frac{Mm}{2k}}$
• B. $T=2\pi \sqrt{\frac{(M+m)}{kmM}}$
• C. $T=2\pi \sqrt{\frac{mM}{2k(M+m)}}$
• D. $T=2\pi \frac{(M+m{)}^2}{k}$

Answer 1

The correct option is C $T=2\pi \sqrt{\frac{mM}{2k(M+m)}}$

Reduced Mass $M=\frac{mM}{m+M}$

$K_{effective}=2K$ [parallel]

$T=2\pi \sqrt{\frac{M}{K}}$

$T=2\pi \sqrt{\frac{mM}{(m+M)2k}}$

$T=2\pi \sqrt{\frac{mM}{2K(M+m)}}$ $\left(C\right)$