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PHY 104 PHY 104 Past Questions Objective Question

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
Options
A √(α/β)
B 2π√(α/β)
Correct Answer
C 2π(α/β)
D 2π(β/α)
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).

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