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A mass on a spring vibrates horizontally on a smooth level surface (see the figure). Its equation of motion is x()-3sin f, where t is in seconds and x in centimeters. Find the velocity at time t. Lonto Ov(t) = sin 3r Ov(1)=2cos 3r O v(1) = cos 31 Ov(t)=3sin 3r Ov(1) = 3cost equilibrium position

A mass on a spring vibrates horizontally on a smooth level surface (see the figure). Its equation of motion is x()-3sin f, where t is in seconds and x in centimeters. Find the velocity at time t. Lonto Ov(t) = sin 3r Ov(1)=2cos 3r O v(1) = cos 31 Ov(t)=3sin 3r Ov(1) = 3cost equilibrium position

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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A mass on a spring vibrates horizontally on a smooth level surface. Its equation of motion is \( x(t) = 3 \sin t \), where \( t \) is in seconds and \( x \) in centimeters. **Find the velocity at time \( t \).** *Diagram Description:* The diagram shows a spring attached to a mass. The spring is depicted with zigzag lines, and it is horizontally aligned with the mass on a surface. The equilibrium position is labeled at the central axis, marked as \( 0 \). *Options for velocity function \( v(t) \):* - \( v(t) = \sin 3t \) - \( v(t) = 2 \cos 3t \) - \( v(t) = \cos 3t \) - \( v(t) = 3 \sin 3t \) - \( v(t) = 3 \cos t \)
Transcribed Image Text:A mass on a spring vibrates horizontally on a smooth level surface. Its equation of motion is \( x(t) = 3 \sin t \), where \( t \) is in seconds and \( x \) in centimeters. **Find the velocity at time \( t \).** *Diagram Description:* The diagram shows a spring attached to a mass. The spring is depicted with zigzag lines, and it is horizontally aligned with the mass on a surface. The equilibrium position is labeled at the central axis, marked as \( 0 \). *Options for velocity function \( v(t) \):* - \( v(t) = \sin 3t \) - \( v(t) = 2 \cos 3t \) - \( v(t) = \cos 3t \) - \( v(t) = 3 \sin 3t \) - \( v(t) = 3 \cos t \)
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