Answer:
Angular frequency ω = 2π / T.
From the diagram, we can see that the time it takes for one complete oscillation or the period T is 2.2 s.
ω = 2π / T
ω = 2(3.14) / 2.2
ω = 2.9 rad s-1
Answer:
The equation given for acceleration is a = - (g / R) x.
The defining equation of simple harmonic motion is a = - ω2x.
We therefore have
g / R = ω2
R = g / ω2
where g is 9.81 m s-2 and ω is the value calculated in (a)
R = 1.2 m
Answer:
We know from Conservation of Energy that the speed of the ball at that point is maximum.
At that maximum speed vO, the displacement is also maximum. This is called amplitude xO.
We can use the formula,
vO = ωxO
vO = 2.9 x 3.0 x 10-2
vO = 0.087 m s-1
Answer:
An example is the following
The orange curve
starts from (3.0 cm, 0 s)
has the same period as the original graph
displacements [including amplitudes] are lower since energy is lost / damping is happening
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