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.

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.

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... Therefore, the system will undergo simple harmonic motion. For such a system, the equation of motion is (see ... come back to its original equilibrium position (x=0 ...

... There is another simple way to understand a harmonic oscillation. Let us consider a particle executing a circular motion with a constant angular velocity ω ...