A block with mass m = 0.3 kg oscillates with amplitude A = 0.4 m at the end of a

Question

A block with mass m = 0.3 kg oscillates with amplitude A = 0.4 m at the end of a spring with force constant k = 5 N/m on a frictionless, horizontal surface. Rank the periods of the following oscillating systems from greatest to smallest. If any periods are equal, show their equality in your ranking. (Use only ">" or "=" symbols. Do not include any parentheses around the letters or symbols.)

(a) The system is as described above.

(b) The amplitude is changed to 0.8 m.

(c) The mass is changed to 0.6 kg.

(d) The spring now has a force constant of 15 N/m.

(e) A small resistive force is added so the motion is underdamped.

Explanation / Answer

force constant k = 5 N/m

mass=0.3 kg

Amplitude=0.4 m

T = 2pi(sqrt(m/k))

a) = 2pi(sqrt (0.3/5)) = 1.54

b) = 2pi(sqrt (0.3/5)) = 1.54 (system unchanged)

c) = 2pi(sqrt (0.6/5)) = 2.17

d) = 2pi(sqrt (0.3/15)) = 0.888

e) w = sqrt ( [k/m] - [b/(2m)]2 ) where b/(2m) < w0 and w0 = sqrt(k/m)

c > e > a = b > d

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