Question 159: Oscillations

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

Accepted Answer

Here, $$x = 2 	imes {10^{ - 2}}\cos \,\pi \,t$$
$$	herefore$$ $$v = {{dx} \over {dt}} = 2 	imes {10^{ - 2}}\,\pi \sin \pi t$$
For the first time, the speed to be maximum,
$$\sin \pi t = 1$$ or, $$\sin \pi t = \sin {\pi  \over 2}$$
$$ \Rightarrow \pi t = {\pi  \over 2}\,\,\,$$ or, $$\,\,\,\,t = {1 \over 2} = 0.5\,\sec .$$

Answer

$$0.25$$ $$s$$

Answer

$$0.5$$ $$s$$

Answer

$$0.75$$ $$s$$

Answer

$$0.125$$ $$s$$

Oscillations

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

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