Monday, September 16, 2019

College Algebra, Chapter 2, 2.5, Section 2.5, Problem 30

The period of a pendulum varies directly with the square root of the length of the pendulum.
a.) Express this relationship by writing an equation.
Let T and be the period of length of the pendulum respectively. So, T=k

b.) To double the period, how would we have to change the length
Let T1 and 1 be the information of the original pendulum. On the other hand, T2 and 2 is the information of the new pendulum.

T1=k1k=T11Equation 1T2=k2Recall that T2=2T12T1=k2k=2T12Equation 2

Use equations 1 and 2 to solve for the requested length.

T11=2T12Cancel out T111=22Apply cross multiplication2=21Square both sides2=41

It shows that, in order to double the period, the length must be four times the original length.

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