Displacement in time

Solving $a = -\omega^2 x$ gives a displacement that varies sinusoidally with time:

\[x(t) = A\cos(\omega t + \phi)\] (1)

$A$ is the amplitude, the furthest the object gets from the middle. $\phi$ is the phase, which just says where in the cycle the clock was started.

If you would rather watch one: a mass on a spring traced against a moving strip of paper.

Check yourself

Have a go. If you get it wrong you will get a hint and one more try; after that we will show you how it works.

Question 1 10 points

Complete the sentence about equation (1).

In x(t) = A cos(ωt + φ), the symbol A is called the and the period of the motion is 2π divided by .

2 attempts left

Question 2 10 points

On the graph below, click the moment where the mass is momentarily at rest — speed zero, about to turn round.

Click the diagram — one place. Click a marker again to remove it.

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