a. Square both sides of Equation 8 and rearrange it to match y = mx + b. b. Writ

Question

a. Square both sides of Equation 8 and

rearrange it to match y = mx + b.

b. Write y = mx + b under your

rearranged equation and circle matching

factors as in the Example.

c. Write two new equations analogous to

Equations 2 and 3 in the Example. Use

the first of the two for calculating k and

the second for finding C from the data of

Fig. 9.

d. A theoretical analysis has shown that for

most springs C = 1/3. Find the percent

error from that value.

e. Derive the units of the slope and

intercept; show that the units of k come

out as N/m and that C is dimensionless.

In Exercise 5 another approach would have been to square both sides of Equation 7 and plot T versus L. Lab 20 directs us to use that alternative. It involves another case of periodic or harmonic motion with a similar, but more complicated, equation for the period: T = 2pi M+Cm2/k (Eq. 8) where T is the period of the bobbing (Fig. 8), M is the suspended mass. ms is the mass of the spring, k is a measure of stiffness called the spring constant, and C is a dimensionless factor showing how much of the spring mass is effectively bobbing. Square both sides of Equation 8 and rearrange it to match y = mx + b. Write y = mx + b under your rearranged equation and circle matching factors as in the Example. Write two new equations analogous to Equations 2 and 3 in the Example. Use the first of the two for calculating k and the second for finding C from the data of Fig. 9. A theoretical analysis has shown that for most springs C = 1/3. Find the percent error from that value. Derive the units of the slope and intercept: show that the units of k come out as N/m and that C is dimensionless.

Explanation / Answer

a) T^2 = 4pi^2M/k + 4pi^2Cm/k

b)y = T^2 , x = M, m = 4pi^2/k , b = 4pi^2Cm/kc)

e)y= mx+bintercept = b so unit of b = metreslope is dimesnionless i.e it has no unitT^2 has unit s^2now each therm on right hand side showuld have unit s^2or, M/k = s^2kg-m/ms^2 = k==> k =N/m

C*m/k = s^2

==> C*kg/kg/s^2 = s^2

==> C*s^2 = s^2

so C is dimensionless

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