PLEASE HELP!! The position of an object connected to a spring varies with time according to the expression x = (4.6 cm) sin(8.9 πt).?
The position of an object connected to a spring varies with time according to the expression x = (4.6 cm) sin(8.9 πt).
(a) Find the period of this motion.
In seconds
(b) Find the frequency of the motion.
In Hz
(c) Find the amplitude of the motion.
In cm
(d) Find the first time after t = 0 that the object reaches the position x = 2.6 cm.
In seconds
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Answers & Comments
y = Asin(bt)
A = amplitude
b = compression/expansion factor.
When b = 1, the period = 2π
If b ≠ 1 , period = (2π / |b|)
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(a) T = period = (2π / b) = (2π / 8.9π) = 0.22 seconds
(b) f = frequency = (1/T) = 4.5 Hz
(c) amplitude = 4.6 cm
(d) Solve for t in
4.6 sin(8.9πt) = 2.6
sin(8.9πt) = (2.6 / 4.6)
8.9πt = sin⁻¹(2.6 / 4.6)
t = [ sin⁻¹(2.6 / 4.6) / 8.9π ]
t ≈ 0.021 seconds
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All of the above answers rounded to 2 significant figures.
Here's a graph of 1 cycle of the function:
(coordinate axes are on different scales)
http://s1164.photobucket.com/user/iago9/media/sin%...