1. A student finds the following values from a graph between M and x in the stat
ID: 2040545 • Letter: 1
Question
1. A student finds the following values from a graph between M and x in the static method of determining the spring constant k: x1 = 0.5 cm, x2 = 7.8 cm; M1 = 120 gm; M2 = 300 gm. Calculate the value of k. 2. Consider the following data for an experiment to study the spring constant by dynamic method: Number of oscillations, N 25 Load M1 120 gm, average time for N oscillations 11.0 seconds Load M2 280 gm; average time for N oscillations 16.9 seconds Calculate the spring constant k (Note that the mass of the hanger is not given.)Explanation / Answer
Q1.
equation of straight line can be given as:
(M-120)/(x-0.5)=(300-120)/(7.8-0.5)=24.658
==>M=120+24.658*(x-0.5)
==>M=107.67+24.658*x
slope=24.658 gram/cm=2.4658 kg/m
but as we know, slope for this graph will be k/g.
hence k/g=2.4658
==>k=2.4658*g
=2.4658*9.8
=24.165 N/m
Q2.
for dynamic method, graph of T^2 vs mass is taken
where T=time period
slope of this graph is given by 4*pi^2/k
where k=spring constant
from the given data, slope of T^2 vs mass line:
(T1^2-T2^2)/(M1-M2)
where T1=11/25=0.44 seconds
T2=16.9/25=0.676 seconds
then slope=1.6461
==>4*pi^2/k=1.6461
==>k=23.983 N/m
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