9. A spring-mass system exhibits free, undamped motion and its position x() is depicted graphically below, where x() is measured in feet and t is measured in seconds. Assume that the mass weighs 8 pounds. Note: The horizontal axis is t and the vertical axis is x(t). Remember that positions below the equilibrium position are considered to be positive. a) Express the motion of the mass in the form x(t) =c₁cos(wt) + c2sin(wt). Give exact values for all quantities. x(t) т ° B t b) What is the initial velocity of the mass? (Exact or a 1 decimal place value is allowed here) c) What is the exact value of k, the spring constant for the system?
9. A spring-mass system exhibits free, undamped motion and its position x() is depicted graphically below, where x() is measured in feet and t is measured in seconds. Assume that the mass weighs 8 pounds. Note: The horizontal axis is t and the vertical axis is x(t). Remember that positions below the equilibrium position are considered to be positive. a) Express the motion of the mass in the form x(t) =c₁cos(wt) + c2sin(wt). Give exact values for all quantities. x(t) т ° B t b) What is the initial velocity of the mass? (Exact or a 1 decimal place value is allowed here) c) What is the exact value of k, the spring constant for the system?
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section5.3: The Natural Exponential Function
Problem 44E
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Transcribed Image Text:9. A spring-mass system exhibits free, undamped motion and its position x() is depicted graphically below, where
x() is measured in feet and t is measured in seconds. Assume that the mass weighs 8 pounds. Note: The horizontal
axis is t and the vertical axis is x(t). Remember that positions below the equilibrium position are considered to be
positive.
a) Express the motion of the mass in the form x(t) =c₁cos(wt) + c2sin(wt). Give exact values for all quantities.
x(t)
т
°
B
t
b) What is the initial velocity of the mass? (Exact or a 1 decimal place value is allowed here)
c) What is the exact value of k, the spring constant for the system?
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