In the figure below, two springs are attached to a block that can oscillate over
ID: 1298155 • Letter: I
Question
In the figure below, two springs are attached to a block that can oscillate over a floor. If the left spring is removed, the block oscillates at a frequency of 26 Hz. If, instead, the spring on the right is removed, the block oscillates at a frequency of 40 Hz. At what frequency does the block oscillate with both springs attached?
In the figure below, two springs are attached to a block that can oscillate over a floor. If the left spring is removed, the block oscillates at a frequency of 26 Hz. If, instead, the spring on the right is removed, the block oscillates at a frequency of 40 Hz. At what frequency does the block oscillate with both springs attached?Explanation / Answer
initially for the left spring
w1=2pif1=sqrt(k1/m)
w1^2=k1/m
===>
k1=m*W1^2
and for the right spring
w2^2=2pif2=k1/m
===>
k2=m*W2^2
now
these two spring are attached in parallel combination
effective spring constant is k'=k1+k2
now
frequency f=1/2pi*sqrt(k'/m)
=1/2pi*sqrt(k1+k2/m)
=1/2pi*sqrt(m*W1^2+m*W2^2/m)
=1/2pi*sqrt(m*(W1^2+W2^2)/m)
=1/2pi*sqrt(W1^2+m*W2^2)
=1/2pi*sqrt((2pi*f1)^2+(2pi*f2)^2)
=1/2pi*2pi*sqrt(f1^2+f2^2)
=sqrt(f1^2+f2^2)
=sqrt(26^2+40^2)
=47.7074 Hz........is answer