In a mechanics laboratory, a 2.5-kilogram mass is suspended from a spring. It is observed that the mass stretches the spring by 16.35 cm. The mass is then pulled 4 cm above its equilibrium position and then, it is released from rest. While the mass is in motion, an external force F(t) = 3cos(rt) is acting. Use g = 9.81 m/s?. Part II А. Determine the value of r that will produce a resonant oscillation of the mass. В. Using the value of r in (A) and the Method of Undetermined Coefficients, write the equation/solution representing the displacement of the mass at any time t, m(t). С. Verify your answer in (B) using the derived solutions for spring-mass systems described as undamped resonance.
In a mechanics laboratory, a 2.5-kilogram mass is suspended from a spring. It is observed that the mass stretches the spring by 16.35 cm. The mass is then pulled 4 cm above its equilibrium position and then, it is released from rest. While the mass is in motion, an external force F(t) = 3cos(rt) is acting. Use g = 9.81 m/s?. Part II А. Determine the value of r that will produce a resonant oscillation of the mass. В. Using the value of r in (A) and the Method of Undetermined Coefficients, write the equation/solution representing the displacement of the mass at any time t, m(t). С. Verify your answer in (B) using the derived solutions for spring-mass systems described as undamped resonance.
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Transcribed Image Text:In a mechanics laboratory, a 2.5-kilogram mass is suspended from a spring.
It is observed that the mass stretches the spring by 16.35 cm. The mass is then pulled 4
cm above its equilibrium position and then, it is released from rest. While the mass is in
motion, an external force F(t) = 3cos(rt) is acting. Use g = 9.81 m/s?.
Part II
A.
Determine the value of r that will produce a resonant oscillation of the mass.
В.
Using the value of r in (A) and the Method of Undetermined Coefficients, write
the equation/solution representing the displacement of the mass at any time t, m(t).
С.
Verify your answer in (B) using the derived solutions for spring-mass systems
described as undamped resonance.
F.
y = Acos(wt) +Bsin(wt) +
tsin(wt)
2mw
D.
Determine the displacement of the mass from its equilibrium position and its
velocity, 5 seconds after it was released from rest.
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