Two springs with negligible masses and force | vedclass

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(D) The two springs are connected in parallel to the block. The effective spring constant $K_{eff}$ is given by $K_{eff} = K_1 + K_2 = 200 + 160 = 360

Vedclass · Accepted Answer

$(A)$ and $(B)$ both.

Vedclass · Answer

(D) The two springs are connected in parallel to the block. The effective spring constant $K_{eff}$ is given by $K_{eff} = K_1 + K_2 = 200 + 160 = 360\, Nm^{-1}$.The angular frequency of oscillation is $\omega = \sqrt{\frac{K_{eff}}{m}} = \sqrt{\frac{360}{10}} = \sqrt{36} = 6\, rad/s$.The period of oscillation is $T = \frac{2\pi}{\omega} = \frac{2\pi}{6} = \frac{\pi}{3} \, s$. Thus,option $(A)$ is correct.The impulse $J$ given to the block provides an initial velocity $v_0$ such that $J = m v_0$. Therefore,$v_0 = \frac{J}{m} = \frac{50}{10} = 5\, ms^{-1}$.Since the block starts from the equilibrium position,the initial velocity is the maximum velocity of the oscillation $(v_{max} = v_0 = 5\, ms^{-1})$. Thus,option $(B)$ is correct.Since both $(A)$ and $(B)$ are correct,the correct option is $(D)$.

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