Question

Two light springs of force constant $k_1$ 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 to rigid supports and the other end is free as shown in the figure. The distance $CD$ between the free ends of the spring is $60cm$. If the block moves along $AB$ with a velocity $120cm/s$ in between the springs, calculate the period of oscillation of the block.
$(k_1=1.8N/m,k_2=3.2N/m,m=200g)$

Answer 1

Time period =time taken by block in between C and D and time taken in moving left from C and right D.

$T=T_0+T_1+T_2$

$=2\times \frac{60}{120}+\frac{1}{2}\times 2\pi \sqrt{\frac{m}{k_1}}+\frac{1}{2}\times 2\pi \sqrt{\frac{m}{k_2}}$

$=1+\pi \sqrt{\frac{0.2}{1.8}}+\pi \sqrt{\frac{0.2}{3.2}}$

$=1+\frac{\pi }{3}+\frac{\pi }{4}=2.8317sec$