Question

A trolley of mass $3$ kg, as shown in figure, is connected to two identical springs, each of spring constant $600N{m}^{-1}$. If the trolley is displaced from its equilibrium position by $5$cm and released, the maximum speed of the trolley is:

• A. $0.5m{s}^{-1}$
• B. $1m{s}^{-1}$
• C. $2m{s}^{-1}$
• D. $3m{s}^{-1}$

Answer 1

The correct option is B $1m{s}^{-1}$

In the given figure, two identical springs are connected in parallel.
$\therefore$ The effective spring constant is
$k_{eff}=2k=2\times 600N{m}^{-1}$
Here, Amplitude, A = $5$cm = 0.05m, $m=3kg$
Angular frequency of oscillation

$\omega =\sqrt{\frac{k_{eff}}{m}}=\sqrt{\frac{1200N{m}^{-1}}{3kg}}=20s^{-1}$

Maximum speed, $v_{max}=A\omega =\left(0.05m\right)\left(20s^{-1}\right)=1m{s}^{-1}$