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

ID: 1448818 • Letter: F

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).

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

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

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

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

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

Explanation / Answer

for a general case, the solution , x=acos(wt) where a= amplitude and w= angular frequency = sqrt(k/m)

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

amplitude= d/2. angular frequency=sqrt(k/M)

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

amplitude= d. angular frequency=sqrt(2k/M)

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

amplitude= d. angular frequency=sqrt(k/M)

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

amplitude= d. angular frequency=sqrt(k/2M)

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

amplitude= 2d. angular frequency=sqrt(2k/M)