It was found that a 31 gram mass hanging from a particular spring had an oscilla

Question

It was found that a 31 gram mass hanging from a particular spring had an oscillation period of 1.5 seconds. (a) When two 31 gram masses are hung from this spring, what would you predict for the period in seconds? New period with two masses = 3.0 (b) When one 31 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 = (c) Suppose that you cut one spring into two equal lengths, and you hang one 31 gram mass from one of these half springs. What would you predict for the period in seconds? New period with half spring- (d) Suppose that you take a single (full-length) spring and a single 31 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

Explanation / Answer

mass, m=31 grams =31*10^-3 kg

time period, T=1.5 sec

T=2pi/w

1.5=2pi/w

===> angular frequency, w=4.2 rad/sec

and

W=sqrt(K/m)

T=2pi*sqrt(m/K)

1.5=2pi*sqrt((31*10^-3)/k)

K=0.54 N/m

a)

T=2pi*sqrt(2m/K)

T=2pi*sqrt(2*31*10^-3/0.54)

==> T=2.13 sec

b)

T=2pi*sqrt(m/2K)

T=2pi*sqrt((31*10^-3)/(2*0.54))

==> T=1.06 sec

c)

T=1.06 sec

d)

T=2pi*sqrt(m/k)

here,

spring constant does not depends on the gravity

hence, T=1.5 sec

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