length = c(108, 89,58,44,25)
period = c(2.080, 1.888, 1.534, 1.3352, 1.0199)
pendulum=data.frame(length, period)
#
#plotting the period versus length data
plot(pendulum$length, pendulum$period,
     main="Pendulum Data",
     xlab="length (cm)",
     ylab="period (s)")
#
# one can obtain use the linear model lm to 
#obtain a power-law fit by taking the log of both 
# x and y variables
pend_fit = lm(log(pendulum$period) ~ 
                log(pendulum$length))
summary(pend_fit)
#
#isolating the power
fit_power=pend_fit$coefficients["log(pendulum$length)"]
fit_power
#
#isolating the coefficient
coeff = exp(pend_fit$coefficients["(Intercept)"])
coeff
#
#displaying the equation
fit_power= round(fit_power,5)
coeff=round(coeff,5)
fit_eq=paste("y=",coeff,"x^",fit_power)
text(40,1.9,fit_eq)
#
#displaying the curve 
curve(coeff*x^fit_power,30,110, add=TRUE, col="blue")