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3. Spring Oscillations A spring hangs from the ceiling at equilibrium with a mass attached to its end. Suppose you pull downward on the mass and release it 10 cm below its equilibrium position with an upward push (see figure below). x>0 Equilibrium- position x=0 x<0 The distance x (in cm) of the mass from its equilibrium position after t seconds is given by the function x(t) = 10 sint - 10 cost, where x is positive when the mass is above the equilibrium position. a) Find the domain of this function within the context of the problem b) Find the range of this function within the context of the problem. c) Graph x(t) within its domain and briefly describe it. d) Calculate x'(t) and explain its meaning. e) Calculate the times when the velocity of the mass is zero.

3. Spring Oscillations A spring hangs from the ceiling at equilibrium with a mass attached to its end. Suppose you pull downward on the mass and release it 10 cm below its equilibrium position with an upward push (see figure below). x>0 Equilibrium- position x=0 x<0 The distance x (in cm) of the mass from its equilibrium position after t seconds is given by the function x(t) = 10 sint - 10 cost, where x is positive when the mass is above the equilibrium position. a) Find the domain of this function within the context of the problem b) Find the range of this function within the context of the problem. c) Graph x(t) within its domain and briefly describe it. d) Calculate x'(t) and explain its meaning. e) Calculate the times when the velocity of the mass is zero.

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.7: Applications
Problem 18EQ
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3. Spring Oscillations A spring hangs from the ceiling at equilibrium with a mass attached to its end. Suppose you pull downward on the mass and release it 10 cm below its equilibrium position with an upward push (see figure below). x>0 Equilibrium- position x=0 x<0 The distance x (in cm) of the mass from its equilibrium position after t seconds is given by the function x(t) = 10 sint - 10 cost, where x is positive when the mass is above the equilibrium position. a) Find the domain of this function within the context of the problem b) Find the range of this function within the context of the problem. c) Graph x(t) within its domain and briefly describe it. d) Calculate x'(t) and explain its meaning. e) Calculate the times when the velocity of the mass is zero.
Transcribed Image Text:3. Spring Oscillations A spring hangs from the ceiling at equilibrium with a mass attached to its end. Suppose you pull downward on the mass and release it 10 cm below its equilibrium position with an upward push (see figure below). x>0 Equilibrium- position x=0 x<0 The distance x (in cm) of the mass from its equilibrium position after t seconds is given by the function x(t) = 10 sint - 10 cost, where x is positive when the mass is above the equilibrium position. a) Find the domain of this function within the context of the problem b) Find the range of this function within the context of the problem. c) Graph x(t) within its domain and briefly describe it. d) Calculate x'(t) and explain its meaning. e) Calculate the times when the velocity of the mass is zero.
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