A body is executing simple harmonic motion. When the displacements from the mean position is 4 cm and 5 cm, the corresponding velocities of the body is 10 cm/sec and 8 cm/sec. Then the time period of the body is (a) 2π sec (b) π/2 sec (c) π sec (d) 3π/2 sec

Answer: (c). 100 = ω²(A² - 16) and 64 = ω²(A² - 25). Subtract: 36 = 9ω² ⇒ ω = 2 rad/s. T = 2π/2 = π s. So the answer is (c) π sec.

A body is executing simple harmonic motion. When the displacements… | NEET 1991 (AIPMT)

Q87NEET 1991 · AIPMTMedium

Velocity & Acceleration in SHM

A body is executing simple harmonic motion. When the displacements from the mean position is $4\text{ cm}$ and $5\text{ cm}$ , the corresponding velocities of the body is $10\text{ cm/sec}$ and $8\text{ cm/sec}$ . Then the time period of the body is

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Answer: (c)

$100 = \omega^2(A^2 - 16)$ and $64 = \omega^2(A^2 - 25)$ .
Subtract: $36 = 9\omega^2 \Rightarrow \omega = 2$ rad/s.
$T = \frac{2\pi}{2} = \pi$ s.
So the answer is (c) $\pi$ sec.

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Velocity & Acceleration in SHM question from NEET 1991 (AIPMT)

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