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1.2.5 Example
The graphs show how the variation with time of the velocity, v and the acceleration, a of a body when it is oscillating with simple harmonic motion.
(a) Determine the period, T.
(b) Sketch the variation with time of the displacement, x, of the oscillating body
[ 2.09 s, x = 2 sin( 3t )]
1.2.5.1 Solution:
a) maximum velocity , v0 = x0ω = 6 m/s
maximum acceleration a0 = x0ω2 = 18 m/s2
thus dividing the 2 equations, we get ω = 3 rad/s
therefore since
b) since maximum velocity , v0 = x0ω = 6 m/s and we now know ω = 3 rad/s earlier
x0(3) = 6
x0 = 2 m
x0 = 2 m
using the model to test check out your answer!
1.2.5.2 Model:
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- Details
- Parent Category: 02 Newtonian Mechanics
- Category: 09 Oscillations
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