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A particle is subjecte to two simple har...

A particle is subjecte to two simple harmonic motions gilven by
`x_1=2.0sin(100pit)and x_2=2.0sin(120pi+pi/3)`, where x is in centimeter and t in second. Find the displacement of the particle at a. t=0.0125, b. t= 0.025.

Text Solution

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The correct Answer is:
A, B, C, D
`x_1=2sin100pit`
`x_2=2sin(120pit+pi/3)`
so, resultant displacement is given by
`x=x_1+x_2`
`=[sin(100pit)+sin(120pit+pi/3)]`
a. At t=0.0125s
`x=2[(sin(100pix0.0125+sin(120ixx0.0125+pi/3))]`
`=2[sin(5pi)/4+sin((3pi)/2)+pi/3]`
`=2[(-0.707)+(-0.5)]`
`=2xx(-1.207)=-2.41cm`
b. At t=0.025s
`x=2[(sin(100pixx0.025)+sin(120pixx0.025+pi/3)]`
`=2[sin((10pi)/4)+sin(3pi+pi/3)]`
`=2[1+(-0.866)]`
`=2xx(0.134)=0.27cm`
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