# Math

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A certain mass is supported by a spring so that it is at rest 0.5 m above a table top. The lowest position of the mass is 0.1 m, and the highest position is 0.9 m. The mass is pulled down 0.4 m at time =0, creating a periodic up and down motion. It takes 1.2 s for the mass to return to the low position each time.

Determine the height of the mass above the table top after 0.7 s.

• physics -

You need to know more than math to answer this question. It is about simple harmonic motion.

The amplitude of oscillation is 0.4 m and the period is 1.2 s.

The vertical height at time t is given by

y = 0.5 - 0.4 cos(2 pi t/1.2)
= 0.5 -0.4 cos(5*pi*t/3)

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