A 2kg object attached to a spring moves without friction and is driven by an external force, given by
$F = 3 \sin (2 πt) N$ . Force constant of the spring is 20 N/m. Amplitude of motion and time period of oscillation respectively are

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7.09 cm , 2 sec

7.09 cm , 1 sec

5.09 cm , 2 sec

5.09 cm , 1 sec

answer is B.

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Detailed Solution

A) $\frac{F_{0} / m}{\sqrt{{(ω_{d}^{2} - ω_{0}^{2})}^{2} + {(\frac{bωd}{m})}^{2}}} where b = 0$
$\begin{array}{l} ω_{0} = \sqrt{\frac{k}{m}} = \sqrt{\frac{20}{2}} = \sqrt{10} {rads}^{- 1} \\ F_{0} = 3 N \\ A = \frac{3 / 2}{\sqrt{{(4 π^{2} - (\sqrt{10})^{2})}^{2} + 0}} = 0 .0509 m \end{array}$
B) Motion taken place with angular frequency of driving force
$ω = ω_{d} = 2 π = \frac{2 π}{T} \Rightarrow T = 1 \sec$