If m represents the motion of a particle executing simple harmonic motion, the amplitude and time period of motion, respectively, are [2024]

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Solution

Q.
If $x = 5 \sin (π t + \frac{π}{3})$ m represents the motion of a particle executing simple harmonic motion, the amplitude and time period of motion, respectively, are [2024]

1 5 cm, 2 s

2 5 m, 2 s

3 5 cm, 1 s

4 5 m, 1 s

Ans.
(2)

Given : $x = 5 \sin (π t + \frac{π}{3}) m$

Comparing the given equation with the standard equation of simple harmonic motion

$x = A \sin (ω t + ϕ)$

we get, A = 5 m and $ω = π$

Time period, $T = \frac{2 π}{ω} = \frac{2 π}{π} = 2$ $s$

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