It was found that a 25 gram mass hanging from a particular spring had an oscilla

Question

It was found that a 25 gram mass hanging from a particular spring had an oscillation period of 1.9 seconds.

(a) When two 25 gram masses are hung from this spring, what would you predict for the period in seconds?
New period with two masses =_____ s

(b) When one 25 gram mass is supported by two of these vertical, parallel springs (see figure), what would you predict for the period in seconds?
New period with two springs =______ s

(c) Suppose that you cut one spring into two equal lengths, and you hang one 25 gram mass from one of these half springs. What would you predict for the period in seconds?
New period with half spring = ______s

(d) Suppose that you take a single (full-length) spring and a single 25 gram mass to the Moon and watch the system oscillate vertically there. What would you predict for the approximate period in seconds? (The gravitational field strength on the Moon is about one-sixth that on the Earth.)
New period on the Moon = _____s

Explanation / Answer

T = 2pi/w >>> T = period
w = sqrt( Ks / m) >>> Ks = spring constant; m = mass

solve for Ks (spring constant) using the formulas given above.
T = 2pi / w
1.9= 2pi / w
w = 3.926

3.926= sqrt ( Ks / m) = sqrt ( Ks / .025)
(3.926)^2 = Ks / .025
Ks = 0.385

(a)
w = sqrt ( .385 / 2(.025)) = 2.77
T = 2pi / 2.77
T = 2.26s

(b)
use the same equations as (a); this time Ks is doubled

(c)
same answer as (b)

(d)
Ks spring stiffness is determined by the material and is not affected or influenced by gravity...a spring on the moon would behave in the same manner as a spring on earth.

Related Questions

Navigate

• Browse (All)
• Browse I
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.