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SHM Graphs

Part of the Mechanics section of Coddy's Physics journey. Lesson 81 of 94.

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

x = A cos(360° · t/T)

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 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 s) and largest at x = 0 (t = 0.5, 1.5 s).

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Challenge

A block on a spring is released from x = A. One third of a period later, when the angle θ in the cosine has reached 120°, the graph shows x = -0.04 m. Find the amplitude A.

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