Question

A trolley of mass $3.0kg$, as shown in figure, is connected to two springs, each of spring has spring constant $600N{m}^{-3}$. If the trolley is displaced from its equilibrium position by $5.0cm$ and released, what is:
a) the period of ensuring oscillations, and
b) the maximum speed of the trolley?

Answer 1

These springs are in parallel (equal displacement)

$=600+600$
$k_{ep}=1200$
(i) $T⟹2\pi \sqrt{\frac{m}{k_{ep}}}⟹2\pi \sqrt{\frac{3}{1200}}$
$=2\pi \sqrt{\frac{1}{400}}$
$=2\times \frac{1}{20}$
$T=\frac{\pi }{10}sec$
(ii) Max speed $⟹Aw$
$=Ax\sqrt{k_{ep}}m$
$=5\times {10}^{-2}\times \sqrt{\frac{1200}{3}}$
$5\times {10}^{-2}\times {10}^{-2}$
$=100\times {10}^{-2}$
$=1m/s$