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angular displacement

angular displacement

Advanced Engineering Mathematics
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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2. When a pendulum 0.5 m long swings back and forth, its angular displacement from rest position, in radians, is given by 8(t)= sin where t is the time, in seconds. At what time(s) during the first 4 s is the pendulum displaced 1 cm vertically above its rest position? (Assume the pendulum is at its rest position at /=0.) ✓✓✓✓✓ length of pendulum = 0.5m radians: 0) = sin(t) cem length of arc = 1 cm Angle 0=0.5m/= Max height: 8am 8:24pm 3. At a certain ocean bay, the maximum height of the water is 4 m above mean sea level at 8:00 a.m. The height is at a maximum again at 8:24 p.m. Assuming that the relationship between the height, h, in metres, and the time, 1, in hours, is sinusoidal, determine the height of the water above mean sea level at 10:00 a.m. ✓✓✓✓✓ 't = 2 0.5×100 A amplititude 3 Period Y = A=²(x-c)) + D 271 phase siri > 12.5 hours 2 A=4m B-12 hours C=O 70
Transcribed Image Text:2. When a pendulum 0.5 m long swings back and forth, its angular displacement from rest position, in radians, is given by 8(t)= sin where t is the time, in seconds. At what time(s) during the first 4 s is the pendulum displaced 1 cm vertically above its rest position? (Assume the pendulum is at its rest position at /=0.) ✓✓✓✓✓ length of pendulum = 0.5m radians: 0) = sin(t) cem length of arc = 1 cm Angle 0=0.5m/= Max height: 8am 8:24pm 3. At a certain ocean bay, the maximum height of the water is 4 m above mean sea level at 8:00 a.m. The height is at a maximum again at 8:24 p.m. Assuming that the relationship between the height, h, in metres, and the time, 1, in hours, is sinusoidal, determine the height of the water above mean sea level at 10:00 a.m. ✓✓✓✓✓ 't = 2 0.5×100 A amplititude 3 Period Y = A=²(x-c)) + D 271 phase siri > 12.5 hours 2 A=4m B-12 hours C=O 70
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