At this stage of the computer experiment, we determine the dependence of the oscillation period of the mathematical pendulum on the amplitude, T(ϕ0), which is described by the formula:
T(ϕ0)=T0(a+bϕ02)
where T0 designates the period of small oscillations of the pendulum, a,b are constant values.
4.1 Calculate the periods of oscillation of the mathematical pendulum for the following set of amplitudes ϕ0: 15°, 30°, 45°, 60°, 75° and 90°, using the value Nmin determined in the previous problem.
4.2 Prove in Graph 3 the applicability of the above formula for the dependence of the oscillation period of the pendulum on its amplitude.
4.3 Determine the values of parameters a,b.
4.4 Let the error in measuring the oscillation period of the pendulum in a real experiment be approximately equal to 5%. Determine at what angles ϕ0, expressed in degrees, the oscillations of the mathematical pendulum can be considered small.