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A block of mass mm is attached to a spring with spring constant kk and is observed to execute damped harmonic motion (no driving force) with its position xx given by x=Ae-ytcos(wt+¢),x=Ae-ytcos(wt+4), with y=7.0y=7.0 s-1–1 and w=27.0w=27.0 s-1-1. Note that y=b/2my=b/2m. (a) If the mass of the block is 6.68 kg find the value of the spring constant kk. (b) The block and spring are now changed to m=0.5m3DO.5 kg and k=389k=389 N/m with the damping the same as in part (a). The block is now driven with a force given by F=(1.25N)cos(wdt+p)F=(1.25N)cos(wdt+p) with wd=29.13wd=29.13 s-1-1 Find the amplitude of the block in meters after the force has been driving the block for several minutes.

A block of mass mm is attached to a spring with spring constant kk and is observed to execute damped harmonic motion (no driving force) with its position xx given by x=Ae-ytcos(wt+¢),x=Ae-ytcos(wt+4), with y=7.0y=7.0 s-1–1 and w=27.0w=27.0 s-1-1. Note that y=b/2my=b/2m. (a) If the mass of the block is 6.68 kg find the value of the spring constant kk. (b) The block and spring are now changed to m=0.5m3DO.5 kg and k=389k=389 N/m with the damping the same as in part (a). The block is now driven with a force given by F=(1.25N)cos(wdt+p)F=(1.25N)cos(wdt+p) with wd=29.13wd=29.13 s-1-1 Find the amplitude of the block in meters after the force has been driving the block for several minutes.

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A block of mass mm is attached to a spring with spring constant kk and is observed to execute damped harmonic motion (no driving force) with its position xx given by x=Ae-ytcos(wi+¢),x=Ae-ytcos(wt+þ), with y=7.0y=7.0 s-1-1 and w=27.0w=27.0 s-1-1. Note that y=b/2my=b/2m. (a) If the mass of the block is 6.68 kg find the value of the spring constant kk. (b) The block and spring are now changed to m=0.5M3D0.5 kg and k=389k=389 N/m with the damping the same as in part (a). The block is now driven with a force given by F=(1.25N)cos(udi+p)F=(1.25N)cos(wdt+4) with wd=29.13wd=29.13 s-1-1 Find the amplitude of the block in meters after the force has been driving the block for several minutes.
Transcribed Image Text:A block of mass mm is attached to a spring with spring constant kk and is observed to execute damped harmonic motion (no driving force) with its position xx given by x=Ae-ytcos(wi+¢),x=Ae-ytcos(wt+þ), with y=7.0y=7.0 s-1-1 and w=27.0w=27.0 s-1-1. Note that y=b/2my=b/2m. (a) If the mass of the block is 6.68 kg find the value of the spring constant kk. (b) The block and spring are now changed to m=0.5M3D0.5 kg and k=389k=389 N/m with the damping the same as in part (a). The block is now driven with a force given by F=(1.25N)cos(udi+p)F=(1.25N)cos(wdt+4) with wd=29.13wd=29.13 s-1-1 Find the amplitude of the block in meters after the force has been driving the block for several minutes.
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