The displacement of an object attached to a spring and executing simple harmonic motion is given by $x = 2 imes 10^{- 2}\cos{\pi t}$ metre. The time at which the maximum speed first occurs is

Question

The displacement of an object attached to a spring and executing simple harmonic motion is given by $x = 2 	imes 10^{- 2}\cos{\pi t}$ metre. The time at which the maximum speed first occurs is

Dr. Abubacker · Accepted Answer

(a) $x = (2 	imes 10^{- 2})\cos{\pi t}$
Here, $a = 2 	imes 10^{- 2}$m = 2 cm
At $t = 0,\ x = 2\ cm$ , $ie$, the object is at positive extreme, so to acquire maximum speed ($ie$, to reach mean position) it takes $\frac{1}{4}$ th of time period.
$	herefore$ Required time = $\frac{T}{4}$
where $\omega = \frac{2\pi}{T} = \pi$
$\Rightarrow \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ T = 2$ s
So, required time = $\frac{T}{4} = \frac{2}{4} = 0.5$ s

Q. The displacement of an object attached to a spring and executing simple harmonic motion is given by $x = 2 \times 10^{- 2}\cos{\pi t}$ metre. The time at which the maximum speed first occurs is

Explanation

Reviewed by Dr. Abubacker

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