Question Detail
Question
The graph between the velocity (v) of a particle executing S.H.M. and its displacement (x) is shown in the figure. The time period of oscillation for this SHM will be
Correct Answer
Option B is the correct answer.
Detailed Explanation
In SHM, the relation between velocity and displacement is v² = ω²(A² - x²). This is an ellipse. The graph shows a straight line with intercepts on the axes. The graph of v vs x is an ellipse, but if it's a straight line, it might be v = -ω² x? Actually, the graph of v vs x for SHM is an ellipse. The maximum velocity v_max = ωA and maximum displacement A. The intercepts on the axes are A and ωA. From the graph, the intercept on the x-axis is α (which is A), and the intercept on the v-axis is β (which is ωA). So ω = β/α. The time period T = 2π/ω = 2πα/β. None of the options match. If the graph is v vs x, the equation is v² = ω²(A² - x²). The intercepts are A and ωA. So β/α = ω. T = 2π/ω = 2πα/β. So T = 2π(α/β). Option C is 2π(α/β).
Hint
The relationship between velocity and displacement in SHM is v² = ω²(A² - x²).