The oscillation of a body on a smooth horizontal surface is represented by x = A cos(ωt), where x is displacement at time t and ω is the angular frequency. Which of the graphs (A)–(D) correctly shows acceleration a versus t over one time period T?
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Question

The oscillation of a body on a smooth horizontal surface is represented by x = A cos(ωt), where x is displacement at time t and ω is the angular frequency. Which of the graphs (A)–(D) correctly shows acceleration a versus t over one time period T?

Options

G1 Physics · Accepted Answer

Step 1: For x = A cos(ωt), SHM acceleration is a(t) = d²x/dt² = −Aω² cos(ωt). Step 2: At t = 0, acceleration is maximum negative: a(0) = −Aω². Step 3: At t = T/4 and 3T/4, acceleration is zero; at t = T/2, it is maximum positive. Step 4: The correct acceleration-time graph starts negative, becomes positive at T/2, and ends negative: option (C). Final answer: (C) Image 3.