Question

An object moves in simple harmonic motion with period 6 seconds and amplitude 4cm. At time =t0 seconds, its displacement d from rest is 0cm, and initially it moves in a negative direction. Give the equation modeling the displacement d as a function of time t.

Answer 1

The general function for describing the displacement from the mean position in harmonic motion is:

`d(t)=A\cdot\sin ((2\pi)/(T)\cdot t+\phi)\text{.}`

Where:

• A is the amplitude,

,

• T is the period,

,

• φ is initial phase displacement.

From the statement, we know that:

• the amplitude is 4 cm,

,

• at time t = 0 its displacement d from the rest is 0 → d(t = 0) = 0,

,

• initially, it moves in a negative direction.

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