# Simple harmonic motion: Position velocity and period

A raft is bobbing up and down in a lake. Its vertical position x above the flat surface of the water is given by x=0.60sin(3.0t+4.2), where distances are in metres and time t is in seconds.

1. What is the boat's position at t=0? At t=2.8s?

2. What is the period of the raft's oscillation?

3. What is the boat's maximum speed during this oscillation?

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#### Solution Preview

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A raft is bobbing up and down in a lake. Its vertical position x above the flat surface of the water is given by x=0.60sin(3.0t+4.2), where distances are in metres and time t is in seconds.

The raft is simply moving up and down and not rotating hence may be considered as a particle in motion.

As the displacement of the raft is a sine function of time its motion is Simple harmonic motion.

The equation of motion of a particle executing simple harmonic motion is given by

x (t) = A sin (t + )

where

A is ...

#### Solution Summary

The equation of motion of the boat in vertical plane is given and the initial position, period and maximum velocity is calculated.