How would the time period change for the mass-spring systemoscillating on the mo

Question

How would the time period change for the mass-spring systemoscillating on the moon? How does the relationship predict that the time will changefor a stiffer spring? How does the relationship predict that the time will changefor a large displacements? How would the time period change for the mass-spring systemoscillating on the moon? How does the relationship predict that the time will changefor a stiffer spring? How does the relationship predict that the time will changefor a large displacements?

Explanation / Answer

1)when the spring is stretched by a distance d from itsinitial position under the action of the load mg.The spring forceis upward,balancing the downward force of gravity mg when thesystem is in equilibrium.The suspended mass is in equilibrium,soset the sum of the forces equal to zero. applying the second law (with a = 0) and solving for thespring constant k: F = Fg + Fs = -ma1 + kd= 0 or k = (ma1/d) here a1 is the acceleration due to gravity onmoon the time period change for the mass-spring system oscillatingon the moon T = 2 * (m/k)^(1/2) = 2 *(m/(ma1/d))^(1/2) = 2 * (m *d/a1)^(1/2) 2)the time period will change for a stiffer spring.This isbecause when the spring is stiffer the vertical displacement of thespring will be smaller and hence the time period will be reduced asT is proportional to d. 3)similarly,for large displacements the time period willincrease according to d.

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