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3. A mass of 0.5 kg hangs from a spring of negligible mass. When an additional mass- of 0.2 kg is attached to the 0.5 kg, the spring is stretched an additional 4 cm. When the 0.2 kg mass is abruptly removed, the amplitude of the resultant vibrations of the 0.5 kg mass is observed to decrease to 1/e its original amplitude in 1 second. (Note: The force on a mass due to gravity = 9.8 x mass.) The resultant displacement is given by the equation: Thi x = A e ³t cos(@dt +ø) where at time t = 0, the decay in amplitude is assumed to be negligible and the displacement x is found to be 3.5cm. Calculate: a). The spring constant, S. b). The mechanical resistance, Rm - Nm- A ing is T= 2m c). The frequency of damped oscillation, @d. d). The phase constant, ø. Rm

3. A mass of 0.5 kg hangs from a spring of negligible mass. When an additional mass- of 0.2 kg is attached to the 0.5 kg, the spring is stretched an additional 4 cm. When the 0.2 kg mass is abruptly removed, the amplitude of the resultant vibrations of the 0.5 kg mass is observed to decrease to 1/e its original amplitude in 1 second. (Note: The force on a mass due to gravity = 9.8 x mass.) The resultant displacement is given by the equation: Thi x = A e ³t cos(@dt +ø) where at time t = 0, the decay in amplitude is assumed to be negligible and the displacement x is found to be 3.5cm. Calculate: a). The spring constant, S. b). The mechanical resistance, Rm - Nm- A ing is T= 2m c). The frequency of damped oscillation, @d. d). The phase constant, ø. Rm

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
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3. A mass of 0.5 kg hangs from a spring of negligible mass. When an additional mass- of 0.2 kg is attached to the 0.5 kg, the spring is stretched an additional 4 cm. When When the 0.2 kg mass is abruptly removed, the amplitude of the resultant vibrations of the 0.5 kg mass is observed to decrease to 1/e its original amplitude in 1 second. (Note: The force on a mass due to gravity = 9.8 x mass.) The resultant displacement is given by the equation: x = A e ³t cos(@at +ø) Thi where at time t = 0, the decay in amplitude is assumed to be negligible and the displacement x is found to be 3.5cm. Calculate: a). The spring constant, S. b). The mechanical resistance, Rm c). The frequency of damped oscillation, @d. d). The phase constant, ø. Nm-hals is T= 2m Rm
Transcribed Image Text:3. A mass of 0.5 kg hangs from a spring of negligible mass. When an additional mass- of 0.2 kg is attached to the 0.5 kg, the spring is stretched an additional 4 cm. When When the 0.2 kg mass is abruptly removed, the amplitude of the resultant vibrations of the 0.5 kg mass is observed to decrease to 1/e its original amplitude in 1 second. (Note: The force on a mass due to gravity = 9.8 x mass.) The resultant displacement is given by the equation: x = A e ³t cos(@at +ø) Thi where at time t = 0, the decay in amplitude is assumed to be negligible and the displacement x is found to be 3.5cm. Calculate: a). The spring constant, S. b). The mechanical resistance, Rm c). The frequency of damped oscillation, @d. d). The phase constant, ø. Nm-hals is T= 2m Rm
d) -Bb At tão, Xo = è Acosø A but So "( 4 cm at t=0, At has decayed minimally Де A cos 0 = 13 3 * ? * Tho is bit strange t e-1t term will е still count from the at which x= know the amplit nah ,ie: X. A J 3. Sem }} ده ) - point oscillations start ارم = 8 | 0.035 0.04 29 Xo A
Transcribed Image Text:d) -Bb At tão, Xo = è Acosø A but So "( 4 cm at t=0, At has decayed minimally Де A cos 0 = 13 3 * ? * Tho is bit strange t e-1t term will е still count from the at which x= know the amplit nah ,ie: X. A J 3. Sem }} ده ) - point oscillations start ارم = 8 | 0.035 0.04 29 Xo A
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