An elastic band is hung on a hook and a mass is hung on the lower end ofthe band. When the mass is pulled downward and then released, itvibrates vertically. The equation of motion is s= 2 cos t+ 3 sin t, t≥0,where s is measured in centimeters and tin seconds. (Take the positivedirection to be downward.) (a) Find the velocity and acceleration at time t.(b) Graph the velocity and acceleration functions.(c) When does the mass pass through the equilibrium position for the first time?(d) How far from its equilibrium position does the mass travel?(e) When is the speed the greatest?
An elastic band is hung on a hook and a mass is hung on the lower end ofthe band. When the mass is pulled downward and then released, itvibrates vertically. The equation of motion is s= 2 cos t+ 3 sin t, t≥0,where s is measured in centimeters and tin seconds. (Take the positivedirection to be downward.) (a) Find the velocity and acceleration at time t.(b) Graph the velocity and acceleration functions.(c) When does the mass pass through the equilibrium position for the first time?(d) How far from its equilibrium position does the mass travel?(e) When is the speed the greatest?
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter6: The Trigonometric Functions
Section6.5: Trigonometric Graphs
Problem 6E
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An elastic band is hung on a hook and a mass is hung on the lower end of
the band. When the mass is pulled downward and then released, it
vibrates vertically. The equation of motion is s= 2 cos t+ 3 sin t, t≥0,
where s is measured in centimeters and tin seconds. (Take the positive
direction to be downward.)
(a) Find the velocity and acceleration at time t.
(b) Graph the velocity and acceleration functions.
(c) When does the mass pass through the equilibrium position for the first time?
(d) How far from its equilibrium position does the mass travel?
(e) When is the speed the greatest?
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