# When an object of mass m1 is hung on a vertical spring and set into vertical simple harmonic motion, its frequency is 12 Hz. When another object of mass m2 is hung on the spring along with m1, the frequency of the motion is 4 Hz. Find the ratio m2/m1 of the masses.

w= sqrt (k/m)

w^2= k/m

(w1/w2)^2=9 = (m1+m2)/m1

9= 1 + m2/m1

check my thinking.

A body is supported by a spiral spring and causes a stretch of 1.5cm in the spring. If the mass is now set in vertical oscillation of small amplitude, what is the periodic time of oscillation

A body is supported by a spiral spring and causes a stretch of 1.5cm in the spring. If the mass is now set in vertical oscillation of small amplitude, what is the periodic time of oscillation

1. frequency f = ω/2π = sqrt(k/m)/2π since k is a constant for the spring.f varies as 1/sqrt(m)

f*sqrt(m) = constant
or
12*sqrt(m1) = 4*sqrt(m1+m2)

simplifying 144*m1 = 16*(m1+m2)

or 144/16 = (m1 + m2)/m1

9 = 1+m2/m1

or m2/m1 = 9 - 1 = 8

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