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)
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