Question

A trolley of mass $3kg$, 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 $5cm$ 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

Answer: (B)

In the given figure, two identical springs are connected in parallel.
$\therefore$ The effective spring constant is
$k_{eff}=2k=2\times 600N{m}^{-1}=1200N{m}^{-1}$
Here, Amplitude, $A=5cm=0.05m,m=3kg$
Angular frequency of oscillation
$\omega =\sqrt{\frac{k_{eff}}{m}}=\sqrt{\frac{1200N{m}^{-1}}{3kg}}=20s^{-1}$
Maximum speed, $v_{\text{max}}=A\omega$
$=(0.05m)(20s^{-1})=1m{s}^{-1}$