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A simple harmonic oscillator consists of a block attached to a spring with k = 200 N/m. The block slides on a frictionless horizontal surface, with equilibrium point x = 0. A graph of the block’s velocity v as a function of time t is shown. Correctly match the required information in the left column with the values (in SI units) given in the right column $(u s e π^{2} = 10)$
Column – I Column – II
A) The block’s mass in kg P) – 0.20
B) The block’s displacement at t = 0 in metres Q) – 200
C) The block’s acceleration at t = 0.10s in $m / s^{2}$ R) 0.20
D) The block’s maximum kinetic energy in Joule S) 4.0

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$A - P, B - Q, C - R, D - S$

$A - S, B - R, C - S, D - P$

$A - R, B - P, C - Q, D - S$

$A - R, B - P, C - S, D - Q$

answer is C.

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Detailed Solution

$V_{m} = A ω \Rightarrow A = \frac{V_{m}}{ω} = \frac{2 π}{2 π} \times (0.2) = 0.20 m$

$T = 2 π \sqrt{\frac{m}{k}} \Rightarrow m = \frac{T^{2} k}{4 π^{2}} = 0.2 k g$

At t = 0.1, acc. is maximum $\Rightarrow = - ω^{2} A \Rightarrow = - 200 m / s^{2}$

Maximum energy $= \frac{1}{2} m V_{m}^{2} = 4 J$

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