A particle of mass 250 g executes a simple harmonic motion under a periodic force . The particle attains a maximum speed of 4 m/s during its oscillation. The amplitude of the motion is ________cm. [2023]

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Solution

Q.
A particle of mass 250 g executes a simple harmonic motion under a periodic force $F = (- 25 x) N$ . The particle attains a maximum speed of 4 m/s during its oscillation. The amplitude of the motion is ________cm. [2023]

Ans.
(40)

$\frac{1}{4} a = - 25 x \Rightarrow a = - 100 x$

$ω^{2} = 100 \Rightarrow ω = 10$

$ω A = 4 \Rightarrow A = \frac{4}{10} = 0.4 m$

$A = 40 cm$

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