Any object or quantity that is moving with a periodic sinusoidal oscillation is said to exhibit simple harmonic motion. This motion can be modeled by the trigonometric function y = A sin(@t) or y = A cos(wt) where A and w are constants. The constant w is called the angular frequency. A mass attached to a spring oscillates upward and downward. The displacement of the mass from its equilibrium position after t seconds is given by the function d = -2.5 cos(4xt), where d is measured in centimeters (see the figure).

Principles of Physics: A Calculus-Based Text
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Chapter12: Oscillatory Motion
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Problem 14P: In an engine, a piston oscillates with simple harmonic motion so that its position varies according...
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Any object or quantity that is moving with a periodic sinusoidal oscillation is said to exhibit simple harmonic motion. This motion can be modeled by the
trigonometric function
y = A sin(@t)
y = A cos(@t)
or
where A and w are constants. The constant w is called the angular frequency.
A mass attached to a spring oscillates upward and downward. The displacement of the mass from its equilibrium position after t seconds is given by the function
d = -2.5 cos(4xt), where d is measured in centimeters (see the figure).
Equilibrium
position
(a) Sketch the graph of this function for 0 <t < 5.
000000000
Transcribed Image Text:Any object or quantity that is moving with a periodic sinusoidal oscillation is said to exhibit simple harmonic motion. This motion can be modeled by the trigonometric function y = A sin(@t) y = A cos(@t) or where A and w are constants. The constant w is called the angular frequency. A mass attached to a spring oscillates upward and downward. The displacement of the mass from its equilibrium position after t seconds is given by the function d = -2.5 cos(4xt), where d is measured in centimeters (see the figure). Equilibrium position (a) Sketch the graph of this function for 0 <t < 5. 000000000
(b) What is the furthest distance of the mass from its equilibrium position?
cm
(c) How long does it take for the mass to complete one oscillation?
sec
Transcribed Image Text:(b) What is the furthest distance of the mass from its equilibrium position? cm (c) How long does it take for the mass to complete one oscillation? sec
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