Question

A 5g body executes SHM with an amplitude of 3 cm and a period of 8 s. What is the force acting on the body 1 s after crossing its mean position? 

          A 5g body executes SHM with an amplitude of 3 cm and a period of 8 s. What is the force acting on the body 1 s after crossing its mean position?

Added by Gerald S.

University Physics with Modern Physics
University Physics with Modern Physics
Hugh D. Young 14th Edition
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A 5g body executes SHM with an amplitude of 3 cm and a period of 8 s. What is the force acting on the body 1 s after crossing its mean position?
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Transcript

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00:01 Here in this question we have given mass of a body equals to 5 gram which can be written as 5 multiply by 10 to the power minus 3 kilogram.
00:21 Also we have amplitude equals to 3 centimeter which can be written as written as 0 .03 meter and we have time period equals to 8 second now we are going to calculate the force acting on the body after crossing its mean position so here we know that expression for the displacement of the body execute simple harmonic motion is given by x of a equals to capital a of small a multiply by sine omega of a multiply by t now the expression for the acceleration of the body is given by a equals to d square of x of a divided by d t square now solving for the acceleration of the body we get a equals to d divided by d t multiply by d divided by d t of d t of a of a sine omega of a multiply by t now on simplifying this, we get a equals to capital a of a, multiply by 2 multiply by pi divided by t, whole square multiply by sign, multiply by 2 multiply by pi divided by small t.
03:00 Here on substituting the value we get a equals to 0 .03 multiply by 2 multiply by pi divided by 8 to the power 2 multiply by sign 2 multiply by pi divided by 1 so now from above we get a equals to 1 .308 multiply by 10 to the power minus 2 meter per second square...
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