Question

Suppose that there is a simulation that shows the period and amplitude change of a pendulum with air resistance included The amount of "friction can control the resistance". It is anticipated that the period decreases.

a) How would you determine if the percent loss of the time period is constant

b )Which of the models could be potentially used to develop a Differential Equation for the period change

c) What would be the independent variable of the model?

Answer 1

a) To determine the percent loss of time period is constant i.e. to determine the period of pendulum decreases by 'A' every 't' unit of time, plot time period of pendulum by the time of observation. One should obtain a straight line plot with negative slope for constant percent loss of time period. This will imply as time of observation increases, the time period decreases.

b) model of damped simple pendulum can be can be used to develop the differential equation for period change. (by inverting the equation d@/dt = (2*g*cos@/l)^0.5 of angular velocity). Then integrate the equation w.r.t. angual displacement '@'.

c) Angular displacement (@) will be the independent variable of the model.

Time will be a dependent variable which is how period change can be calculated in b)