Five different experiments are carried out. In each experiment, a block is attac

Question

Five different experiments are carried out. In each experiment, a block is attached to a horizontal spring. The block is pulled back a certain distance and released. The block oscillates back and forth on a frictionless surface. Rank the amplitude of oscillation for each of the following situations. (Rank the smallest amplitude as 1).

-A block of mass 2M is attached to a spring with a spring constant k, pulled back a distance d, and released.

-A block of mass M is attached to a spring with a spring constant k, pulled back a distance d, and released.

-A block of mass M is attached to a spring with a spring constant 2k, pulled back a distance (1/2)d, and released.

-A block of mass M is attached to a spring with a spring constant (1/2)k, pulled back a distance d, and released.

-A block of mass M is attached to a spring with a spring constant k, pulled back a distance (1/2)d, and released.

Explanation / Answer

The maximum force on the block can be calculated using the Hooke's law F = kx Here, k is the spring constant and x is the compression or stretched distance

i) Spring constant is k , stretched distance is d/2 F1 = k (d/2) =1/2 (kd)           Rank - (1)

ii) Spring constant is 2k , stretched distance is 2d F2 = 2k (2d) 4 (kd)             Rank - (3)

iii) Spring constant is 1/2k , stretched distance is d F3 = 1/2k (d) = 1/2 (kd)         Rank - (1)

iv)Spring constant is k , stretched distance is d F4 = k (d) = kd                 Rank - (2)   

v)Spring constant is k , stretched distance is d F5 = k (d) = kd                   Rank - (2)   

F2 > (F4 =  F5) > ( F1 = F3 )   

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