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 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 2k, pulled back a distance (1/2)d, and released.
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 (1/2)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.

please rank in order

Explanation / Answer

Time period of Oscillation T = 2pi sqrt(m/k)

T is proportional to sqrt(m/k)

case 1: T1 = sqrt(M/2K) = 0.707 sqrt(m/k)

case 2 : T2 = sqrt(M/k) = 1 * sqrt (m/k)

case 3: T3 = sqrt(2M/k) = 1.414 sqrt(m/k)

case4 : T4 = sqrt(m/k) = sqrt(m/k)

case 5: T5 = sqrt(M/k) = sqrt(m/k)

so order increasing order exps is

3 > 2> 1 > 4 = 5

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