A mass of 85 grams stretches a spring by 9 cm. (Note that this means the forces balance, and thus mg = kx where m = 85 grams is mass, g = 981 cm/s is acceleration due to gravity, k is the spring constant, and x = 9 cm is the displacement.) The mass is set in motion from this equilibrium position with an initial downward velocity of 22 cm/s, and there is no damping. Find the position u (in cm) of the mass at any time t (in s). (Assume that position is measured upward from the equilibrium position.) u(t) = Find the frequency (in radians per second), period (in seconds), and amplitude (in cm) of the motion. Frequency is Period is Amplitude is
A mass of 85 grams stretches a spring by 9 cm. (Note that this means the forces balance, and thus mg = kx where m = 85 grams is mass, g = 981 cm/s is acceleration due to gravity, k is the spring constant, and x = 9 cm is the displacement.) The mass is set in motion from this equilibrium position with an initial downward velocity of 22 cm/s, and there is no damping. Find the position u (in cm) of the mass at any time t (in s). (Assume that position is measured upward from the equilibrium position.) u(t) = Find the frequency (in radians per second), period (in seconds), and amplitude (in cm) of the motion. Frequency is Period is Amplitude is
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:, A mass of 85 grams stretches a spring by 9 cm. (Note that this means the forces balance, and thus mg
kx where m = 85 grams is mass,
g = 981 cm/s is acceleration due to gravity, k is the spring constant, and x = 9 cm is the displacement.)
The mass is set in motion from this equilibrium position with an initial downward velocity of 22 cm/s, and there is no damping. Find the position u (in cm)
of the mass at any time t (in s). (Assume that position is measured upward from the equilibrium position.)
u(t)
=
Find the frequency (in radians per second), period (in seconds), and amplitude (in cm) of the motion.
Frequency is
Period is
Amplitude is
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