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SHM Graphs

Part of the Mechanics section of Coddy's Physics journey. Lesson 84 of 97.

Released from x=A\relax x = A, the block's x-t graph is a cosine:

x=Acos⁡(360∘⋅tT)x = A\cos\left(360^\circ \cdot \frac{t}{T}\right)

A displacement-time graph of an oscillator: a cosine curve starting at 0.1 metres at t = 0, down through 0 at 0.5 seconds to minus 0.1 metres at 1 second, and back to 0.1 metres at 2 seconds

x-t: released at x = A, the block is back at A after one period, 2 s2\ \mathrm{s}.

Peak height: the amplitude. Peak to peak: the period.

The velocity is zero at the turning points and largest where the block passes equilibrium.

A velocity-time graph of the same oscillator: zero at t = 0, down to minus 0.31 metres per second at 0.5 seconds, back to zero at 1 second and up to 0.31 metres per second at 1.5 seconds

v-t: the speed is zero at the ends (t = 0, 1, 2 s2\ \mathrm{s}) and largest at x = 0 (t = 0.5, 1.5 s1.5\ \mathrm{s}).

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Challenge

A block on a spring is released from x=A\relax x = A. One third of a period later, when the angle θ\theta in the cosine has reached 120∘120^\circ, the graph shows x=−0.04 mx = -0.04\ \mathrm{m}. Find the amplitude AA.

Try it yourself

Physics diagram: plot, ball

Solve for AA

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