A block is attached to a spring and set in motion on a horizontal frictionless s

Question

A block is attached to a spring and set in motion on a horizontal frictionless surface by pulling the block back a distance 10cm from equilibrium. Now, replace the block with one double the mass and set the block into motion again by pulling the block a distance 10cm from equilibrium and releasing. How will the following new quantities relate to the quanities with the original block? (If it will be larger by a factor of 2, choose double. sqrt stands for square root.)

choose from ( quarter, half, sqrt(1/2), same, sqrt(2), double, quadruple)

Maximum Acceleration

Maximum Force of the Spring on the Block

Period of oscillation

Amplitude

Explanation / Answer

max accn in the first case = ^2 A = kA / m = a

max accn in the second case = '^2 A = kA / [ 2 m ] = a' = a / 2

so the new accn becomes half of the original <-----------ans for accn

F = -kA , original case ,

F = - kA , second case , sicne the amplitude reamains unchanged .

so new force is same as before <------------ans for force

T = 2 ( m / k ) in the first case ,

T ' =  2 ( 2m / k ) in the 2nd case ,

T ' = 2 [ 2 ( m / k ) ] ;

T ' = 2 T ,

so the new time period is 2 times the original <---------ans for time period ,

the amplitude remains unchanged since both the object are pulled the same distance from the

equilibrium position <-----------ans for amplitude   

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