Simple harmonic motion: Position velocity and period
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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.
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 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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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 ...
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